The table of contents below is very preliminary. Many chapters are already at my home page as pdf files although their form will not be final: for instance, introduction must be expanded. If You want, say chapter "Construction of Quantum Theory", as a .pdf file, just click on "Construction of Quantum Theory" in the table of contents. To help the reader to get overview I have included also a list of links to the chapters in the table of contents as well as corresponding abstracts. Most of the abstract files are also already there.



TOPOLOGICAL GEOMETRODYNAMICS: AN OVERVIEW



||Introduction||
PART I: GENERAL OVERVIEW
||Topological Geometrodynamics: What Might Be the First Principles?||An Overview about the Evolution of TGD||An Overview about Quantum TGD|| TGD and M-Theory ||
PART II: PHYSICS AS INFINITE-DIMENSIONAL SPINOR GEOMETRY IN THE WORLD OF CLASSICAL WORLDS
|| Classical TGD|| The Geometry of the World of the Classical Worlds|| Configuration Space Spinor Structure ||
PART III: ALGEBRAIC PHYSICS
TGD as a Generalized Number Theory I: p-Adicization Program||TGD as a Generalized Number Theory II: Quaternions, Octonions, and their Hyper Counterparts||TGD as a Generalized Number Theory III: Infinite Primes||
PART IV: HYPERFINITE FACTORS OF TYPE II1 AND HIERARCHY OF PLANCK CONSTANTS
||Was von Neumann Right After All?||Does TGD Predict the Spectrum of Planck Constants?||
PART V: APPLICATIONS
||Cosmology and Astrophysics in Many-Sheeted Space-Time ||Elementary Particle Vacuum Functionals||Massless States and Particle Massivation||
||Appendix||



Introduction

  1. Basic ideas of TGD

    1. TGD as a Poincare invariant theory of gravitation

    2. TGD as a generalization of the hadronic string model

    3. Fusion of the two approaches via a generalization of the space-time concept

  2. The five threads in the development of quantum TGD

    1. Quantum TGD as configuration space spinor geometry

    2. p-Adic TGD

    3. TGD as a generalization of physics to a theory consciousness

    4. TGD as a generalized number theory

    5. Dynamical quantized Planck constant and dark matter hierarchy

    6. The contents of the book

      1. PART I: General Overview

      2. PART II: Physics as infinite-dimensional spinor geometry in the world of classical worlds

      3. PART III: Algebraic Physics

      4. PART IV: HYPERFINITE FACTORS OF TYPE II1 AND HIERARCHY OF PLANCK CONSTANTS

      5. PART V: Applications



PART I: GENERAL OVERVIEW



HomeAbstract

    Topological Geometrodynamics: What might be the First Principles?

  1. Introduction

  2. What might be the first principles of quantum TGD

    1. From Equivalence Principle to zero energy ontology

    2. Physics as a physics of classical spinor fields in the world of classical worlds?

    3. Is the dynamics of quantum TGD fixed from lightlikeness of 3-surfaces?

    4. Physics as a generalized number theory?

    5. Configuration space gamma matrices as hyper-octonionic conformal fields having values in HFF?

    6. Hierarchy of Planck constants and quantum criticality

    7. Does the finiteness of measurement resolution dictate the laws of physics?

    8. Are both symplectic and conformal field theories be needed? /font>

  3. What are the basic equations of quantum TGD

  4. Some applications

    1. p-Adic mass calculations

    2. Cosmology and astrophysics

    3. Hierarchy of scaled variants of standard model physics

    4. Quantum TGD and biology

  5. Where are we now?



HomeAbstract

    Overall View About Evolution of TGD

  1. Introduction

  2. Evolution of classical TGD

    1. Quantum classical correspondence and why classical TGD is so important?

    2. Classical fields

    3. Many-sheeted space-time concept

    4. Classical non-determinism of Kähler action

    5. Quantum classical correspondence as an interpretational guide

  3. Evolution of p-adic ideas

    1. p-Adic numbers

    2. Evolution of physical ideas

    3. Evolution of mathematical ideas

    4. Generalized Quantum Mechanics

    5. Do state function reduction and state-preparation have number theoretical origin?

  4. The boost from TGD inspired theory of consciousness

    1. The anatomy of the quantum jump

    2. Negentropy Maximization Principle and new information measures

  5. TGD as a generalized number theory

    1. The painting is the landscape

    2. p-Adic physics as physics of cognition

    3. Space-time-surface as a hyper-quaternionic sub-manifold of hyper-octonionic imbedding space?

    4. Infinite primes and physics in TGD Universe

    5. Infinite primes and more precise view about p-adic length scale hypothesis

    6. Infinite primes, cognition, and intentionality

    7. Complete algebraic, topological, and dimensional democracy?



HomeAbstract

    Overall View about Quantum TGD

  1. Introduction

    1. Geometric ideas

    2. Ideas related to the construction of S-matrix

    3. Some general predictions of TGD

  2. Physics as geometry of configuration space spinor fields

    1. Reduction of quantum physics to the Kähler geometry and spinor structure of configuration space of 3-surfaces

    2. Constraints on configuration space geometry

    3. Configuration space as a union of symmetric spaces

    4. An educated guess for the Kähler function

    5. An alternative for the absolute minimization of Kähler action

    6. The construction of the configuration space geometry from symmetry principles

    7. Configuration space spinor structure

    8. What about infinities?

  3. Identification of elementary particles and the role of Higgs in particle massivation

    1. Identification of elementary particles

    2. New view about the role of Higgs boson in massivation

    3. General mass formulas

  4. Von Neumann algebras and TGD

    1. Philosophical ideas behind von Neumann algebras

    2. Von Neumann, Dirac, and Feynman

    3. Factors of type II1 and quantum TGD

    4. Does TGD emerge from a local variant of infinite-dimensional Clifford algebra?

    5. Quantum measurement theory with a finite measurement resolution

    6. The generalization of imbedding space concept and hierarchy of Planck constants

    7. Cognitive consciousness, quantum computations, and Jones inclusions

    8. Fuzzy quantum logic and possible anomalies in the experimental data for EPR-Bohm experiment

  5. Hierarchy of Planck constants and the generalization of the notion of imbedding space

    1. The evolution of physical ideas about hierarchy of Planck constants

    2. The most general option for the generalized imbedding space

    3. About the phase transitions changing Planck constant

    4. How one could fix the spectrum of Planck constants?

    5. Preferred values of Planck constants

    6. How Planck constants are visible in Kähler action?

    7. A simple model for fractional quantum Hall effect

    8. The identification of number theoretic braids

  6. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Minimal form of M8-H duality

    3. Strong form of M8-H duality

    4. M8-H duality and low energy hadron physics

    5. Connection with string model and Equivalence Principle at space-time level

  7. Does the modified Dirac action define the fundamental action principle?

    1. Modified Dirac equation

    2. Quantum criticality and modified Dirac equation

    3. Handful of problems with a common resolution

  8. Could one generalize the notion of twistor to 8-D case?

    1. Octo-twistors defined in terms of ordinary spinors

    2. Could right handed neutrino spinor modes define octo twistors?

    3. Octo-twistors and modified Dirac equation

    4. What one really means with virtual particle?

  9. Super-symmetries at space-time and configuration space level

    1. Configuration space as a union of symmetric spaces

    2. Isometries of configuration space as symplectic transformations of δ M4+/-× CP2

    3. SUSY algebra defined by the anticommutation relations of fermionic oscillator operators and WCW local Clifford algebra elements as chiral super-fields

    4. Identification of Kac-Moody symmetries

    5. Coset space structure for configuration space as symmetric space

    6. Comparison of TGD and string views about super-conformal symmetries

  10. About the construction of S-matrix

    1. About the general conceptual framework behind quantum TGD

    2. S-matrix as a functor in TQFTs

    3. S-matrix as a functor in quantum TGD

    4. Finite measurement resolution: from S-matrix to quantum S-matrix

    5. Number theoretic constraints on S-matrix

    6. Does Connes tensor product fix the allowed M-matrices?

    7. Summary about the construction of S-matrix

  11. General vision about coupling constant evolution

    1. General ideas about coupling constant evolution

    2. Both symplectic and conformal field theories are needed in TGD framework

  12. The recent view about p-adic coupling constant evolution

    1. The bosonic action defining Kähler function as the effective action associated with the induced spinor fields

    2. A revised view about coupling constant evolution

  13. QFT limit of TGD

    1. Twistors and QFT limit of TGD

    2. Bosonic emergence and QFT limit of TGD



HomeAbstract

    TGD and M-Theory

  1. Introduction

    1. From hadronic string model to M-theory

    2. Evolution of TGD briefly

  2. A summary about the evolution of TGD

    1. Space-times as 4-surfaces

    2. Uniqueness of the imbedding space from the requirement of infinite-dimensional Kähler geometric existence

    3. TGD inspired theory of consciousness and other developments

    4. Von Neumann algebras and TGD

    5. Does dark matter at larger space-time sheets define super-quantal phase?

  3. Quantum TGD in nutshell

    1. Geometric ideas

    2. The notions of imbedding space, 3-surface, and configuration space

    3. The construction of M-matrix

  4. Victories of M-theory from TGD view point

    1. Superconformal symmetries

    2. Dualities

    3. Dualities and conformal symmetries in TGD framework

    4. Number theoretic compactification and M8 duality

    5. Configuration space gamma matrices as hyper-octonionic conformal fields and number theoretic braids

    6. Black hole physics

    7. Zero energy ontology and Witten's approach to 3-D quantum gravitation

  5. What went wrong with string models?

    1. Problems of M-theory

    2. Mouse as a tailor

    3. The dogma of reductionism

    4. The loosely defined M

    5. Los Alamos, M-theory, and TGD



PART II: PHYSICS AS INFINITE-DIMENSIONAL SPINOR GEOMETRY IN THE WORLD OF CLASSICAL WORLDS



HomeAbstract

    Classical TGD

  1. Introduction

    1. Quantum-classical correspondence

    2. Classical physics as exact part of quantum theory

    3. Some basic ideas of TGD inspired theory of consciousness and quantum biology

  2. Many-sheeted space-time, magnetic flux quanta, electrets and MEs

    1. Dynamical quantized Planck constant and dark matter hierarchy

    2. p-Adic length scale hypothesis and the connection between thermal de Broglie wave length and size of the space-time sheet

    3. Topological light rays (massless extremals, MEs)

    4. Magnetic flux quanta and electrets

  3. General considerations

    1. Number theoretical compactification and M8-H duality

    2. The exponent of Kähler function as Dirac determinant for the modified Dirac action

    3. Preferred extremal property as classical correlate for quantum criticality, holography, and quantum classical correspondence

  4. General view about field equations

    1. Field equations

    2. Could Lorentz force vanish identically for all extremals/absolute minima of Kähler action?

    3. Topologization of the Kähler current as a solution to the generalized Beltrami condition

    4. How to satisfy field equations?

    5. D=3 phase allows infinite number of topological charges characterizing the linking of magnetic field lines

    6. Preferred extremal property and the topologization/light-likeness of Kähler current?

    7. Generalized Beltrami fields and biological systems

    8. About small perturbations of field equations

  5. Basic extremals of Kähler action

    1. CP2 type vacuum extremals

    2. Vacuum extremals with vanishing Kähler field

    3. Cosmic strings

    4. Massless extremals

    5. Generalization of the solution ansatz defining massless extremals (MEs)



HomeAbstract

    The geometry of the world of the classical worlds

  1. The quantum states of Universe as modes of classical spinor field in the "world of classical worlds"

    1. Definition of Kähler function

    2. Minkowski space or its light cone?

    3. Configuration space metric from symmetries

    4. What principle selects the preferred extremals?

  2. Constraints on the configuration space geometry

    1. Configuration space as "the world of classical worlds"

    2. Diff4 invariance and Diff4 degeneracy

    3. Decomposition of the configuration space into a union of symmetric spaces G/H

    4. Kähler property

  3. Construction of configuration space geometry from Kähler function

    1. Definition of Kähler function

    2. Minkowski space or its light cone?

    3. The values of Kähler coupling strength

    4. Absolute minimization or something else?

  4. Construction of configuration space Kähler geometry from symmetry principles

    1. General Coordinate Invariance and generalized quantum gravitational holography

    2. Light like 3-D causal determinants, 7-3 duality, and effective 2-dimensionality

    3. Magic properties of light cone boundary and isometries of configuration space

    4. Canonical transformations of δ M4+× CP2 as isometries of configuration space

    5. Symmetric space property reduces to conformal and canonical invariance

    6. Magnetic Hamiltonians

    7. Electric Hamiltonians and electric-magnetic duality

  5. How to generalize the construction of configuration space geometry to take into account the classical non-determinism?

    1. Quantum holography in the sense of quantum gravity theories

    2. How the classical determinism fails in TGD?

    3. The notions of imbedding space, 3-surface, and configuration space

    4. The treatment of non-determinism of Kähler action in zero energy ontology

  6. Exponent of Kähler function as Dirac determinant for the modified Dirac action

    1. How to define Dirac determinant?

    2. Dirac determinant as a product of eigenvalues for the transverse part of DK

    3. Representation of configuration Kähler metric in terms of eigenvalues of DC-S

  7. Ricci flatness and divergence cancellation

    1. Inner product from divergence cancellation

    2. Why Ricci flatness

    3. Ricci flatness and Hyper Kähler property

    4. The conditions guaranteing Ricci flatness

    5. Is configuration space metric Hyper Kähler?



HomeAbstract

    Configuration Space Spinor Structure

  1. Introduction

    1. Geometrization of fermionic statistics in terms of configuration space spinor structure

    2. Modified Dirac equation for induced classical spinor fields

    3. The exponent of Kähler function as Dirac determinant for the modified Dirac action?

    4. Super-conformal symmetries

  2. Configuration space spinor structure: general definition

    1. Defining relations for γ matrices

    2. General vielbein representations

    3. Inner product for configuration space spinor fields

    4. Holonomy group of the vielbein connection

    5. Realization of configuration space γ matrices in terms of super symmetry generators

    6. Central extension as symplectic extension at configuration space level

    7. Configuration space Clifford algebra as a hyper-finite factor of type II1

  3. Generalization of the notion of imbedding space

    1. Generalization of the notion of imbedding space

    2. Phase transitions changing the value of Planck constant

  4. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Hyper-octonionic Pauli "matrices" and modified definition of hyper-quaternionicity

    3. Minimal form of M8-H duality

    4. Strong form of M8-H duality

    5. M8-H duality and low energy hadron physics

    6. The notion of number theoretic braid

    7. Connection with string model and Equivalence Principle at space-time level

  5. Does the modified Dirac action define the fundamental action principle?

    1. Modified Dirac equation

    2. Quantum criticality and modified Dirac equation

    3. Handful of problems with a common resolution

  6. Representations for the configuration space γ matrices in terms of super-symplectic charges at light cone boundary

    1. Magnetic flux representation of the super-symplectic algebra

    2. Quantization of the modified Dirac action

    3. Expressions for super-symplectic generators in finite measurement resolution

  7. Super-symmetries at space-time and configuration space level

    1. Configuration space as a union of symmetric spaces

    2. Isometries of configuration space geometry as symplectic transformations of δM4+/- × CP2

    3. SUSY algebra defined by the anticommutation relations of fermionic oscillator operators and WCW local Clifford algebra elements as chiral super-fields

    4. Identification of Kac-Moody symmetries

    5. Coset space structure for configuration space as a symmetric space

    6. The relationship between super-symplectic and Super Kac-Moody algebras, Equivalence Principle, and justification of p-adic thermodynamics

    7. Comparison of TGD and stringy views about super-conformal symmetries

    8. Could the notion of super-space make sense in TGD framework?



PART III: ALGEBRAIC PHYSICS



HomeAbstract

    TGD as a Generalized Number Theory I: p-Adicization Program

  1. Introduction

    1. The painting is the landscape

    2. Real and p-adic regions of the space-time as geometric correlates of matter and mind

    3. The generalization of the notion of number

    4. Zero energy ontology, cognition, and intentionality

    5. p-Adicization by algebraic continuation

  2. How p-adic numbers emerge from algebraic physics?

    1. Basic ideas and questions

    2. Are more general adics indeed needed?

    3. Why completion to p-adics necessarily occurs?

    4. Decomposition of space-time to ...-adic regions

    5. Universe as an algebraic hologram?

    6. How to assign a p-adic prime to a given real space-time sheet?

    7. Gaussian and Eisenstein primes and physics

    8. p-Adic length scale hypothesis and hyper-quaternionic and -octonionic primality

  3. Scaling hierarchies and physics as a generalized number theory

    1. p-Adic physics and the construction of solutions of field equations

    2. A more detailed view about how local p-adic physics codes for p-adic fractal long range correlations of the real physics

    3. Cognition, logic, and p-adicity

    4. Fibonacci numbers, Golden Mean, and Jones inclusions

  4. The recent view about p-adic coupling constant evolution

    1. The bosonic action defining Kähler function as the effective action associated with the induced spinor fields

    2. A revised view about coupling constant evolution

  5. The quantum dynamics of topological condensation and connection with string models

    1. Questions related to topological condensation

    2. Super-conformal invariance and new view about energy as solution of the problems

    3. Connection with string models and how gravitational constant appears

    4. Elementary particle vacuum functionals and gravitational conformal invariance

    5. Questions about topological condensation

  6. Algebraic physics at the level of configuration space

    1. A possible view about basic problems

    2. Algebraic physics and configuration space geometry

    3. Generalizing the construction of the configuration space geometry to the p-adic context

    4. p-Adicization of quantum TGD by algebraic continuation

    5. Minimal approach: p-adicize only the reduced configuration space

    6. The most recent vision about zero energy ontology and p-adicization

  7. Appendix: Basic facts about algebraic numbers, quaternions and octonions

    1. Generalizing the notion of prime

    2. UFDs, PIDs and EDs

    3. The notion of prime ideal

    4. Examples of two-dimensional algebraic number fields

    5. Cyclotomic number fields as examples of four-dimensional algebraic number fields

    6. Quaternionic primes

    7. Imbedding space metric and vielbein must involve only rational functions



HomeAbstract

    TGD as a Generalized Number Theory II: Quaternions, Octonions, and their Hyper Counterparts

  1. Introduction

    1. Hyper-octonions and hyper-quaternions

    2. Number theoretical compactification and M8-H duality

    3. Romantic stuff

    4. Notations

  2. Quaternion and octonion structures and their hyper counterparts

    1. Motivations and basic ideas

    2. Octonions and quaternions

    3. Hyper-octonions and hyper-quaternions

    4. p-Adic length scale hypothesis and quaternionic and hyper-quaternionic primes

    5. Manifolds with (hyper-)octonion and (hyper-)quaternion structure

    6. Light-like causal determinants, number theoretic light-likeness, and generalization of residue calculus

    7. Induction of the (hyper-)octonionic structure

  3. Quantum TGD in nutshell

    1. Geometric ideas

    2. The notions of imbedding space, 3-surface, and configuration space

    3. The construction of M-matrix

  4. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Minimal form of M8-H duality

    3. Strong form of M8-H duality

    4. M8-H duality and low energy hadron physics

    5. The notion of number theoretical braid

  5. Quaternions, octonions, and modified Dirac equation

    1. The replacement of SO(7,1) with G2

    2. Octonionic counterpart of the modified Dirac equation

    3. Could the notion of octo-twistor make sense?

  6. Configuration gamma matrices as hyper-octonionic conformal fields and number theoretic braids

    1. Only the quantum variants of M4 and M8 emerge from local hyper-finite II1 factors

    2. Configuration space spinor fields as hyper-octonionic conformal fields

  7. E8 theory of Garrett Lisi and TGD

    1. Objections against Lisi's theory

    2. Three attempts to save Lisi's theory

    3. Could super-symmetry rescue the situation?

    4. Could Kac Moody variant of E8 make sense in TGD?

    5. Can one interpret three fermion families in terms of E8 in TGD framework?



HomeAbstract

    TGD as a Generalized Number Theory III: Infinite Primes

  1. Introduction

    1. The notion of infinite prime

    2. Generalization of ordinary number fields

    3. Infinite primes and physics in TGD Universe

    4. About literature

  2. Infinite primes, integers, and rationals

    1. The first level of hierarchy

    2. Infinite primes form a hierarchy

    3. Construction of infinite primes as a repeated quantization of a super-symmetric arithmetic quantum field theory

    4. Construction in the case of an arbitrary commutative number field

    5. Mapping of infinite primes to polynomials and geometric objects

    6. How to order infinite primes?

    7. What is the cardinality of infinite primes at given level?

    8. How to generalize the concepts of infinite integer, rational and real?

    9. Comparison with the approach of Cantor

  3. Generalizing the notion of infinite prime to the non-commutative context

    1. General view about the construction of generalized infinite primes

    2. Quaternionic and octonionic primes and their hyper counterparts

    3. Hyper-octonionic infinite primes

    4. Mapping of the hyper-octonionic infinite primes to polynomials

  4. The representation of hyper-octonionic infinite primes as space-time surfaces

    1. Hyper-quaternionic 4-surfaces in HO correspond to space-time surfaces in M4× CP2

    2. Integrability conditions

    3. How to solve the integrability conditions?

    4. About the physical interpretation of the solution ansatz

    5. Mapping of infinite primes to space-time surfaces

  5. How to interpret the infinite hierarchy of infinite primes?

    1. Infinite primes and hierarchy of super-symmetric arithmetic quantum field theories

    2. Prime Hilbert spaces and infinite primes

    3. Do infinite hyper-octonionic primes represent quantum numbers associated with Fock states?

    4. The physical interpretation of infinite integers at the first level of the hierarchy

    5. What is the interpretation of the higher level infinite primes?

    6. Infinite primes and the structure of many-sheeted space-time

    7. How infinite integers could correspond to p-adic effective topologies?

    8. An alternative interpretation for the hierarchy of functions defined by infinite primes

  6. Does the notion of infinite-P p-adicity make sense?

    1. Does infinite-P p-adicity reduce to q-adicity?

    2. q-Adic topology determined by infinite prime as a local topology of the configuration space

    3. The interpretation of the discrete topology determined by infinite prime

  7. Infinite primes and mathematical consciousness

    1. Infinite primes, cognition and intentionality

    2. Algebraic Brahman=Atman identity

    3. The generalization of the notion of ordinary number field

    4. One element field, quantum measurement theory and its q-variant, and the Galois fields associated with infinite primes

    5. Leaving the world of finite reals and ending up to the ancient Greece

    6. Infinite primes and mystic world view

    7. Infinite primes and evolution

  8. Local zeta functions, Galois groups, and infinite primes

    1. Local zeta functions and Weil conjectures

    2. Local zeta functions and TGD

    3. Galois groups, Jones inclusions, and infinite primes

  9. Remarks about correspondence between infinite primes , space-time surfaces, and configuration space spinor fields

    1. How CH and CH spinor fields correspond to infinite rationals?

    2. Can one understand fundamental symmetries number theoretically?

  10. A little crazy speculation about knots and infinite primes

    1. Do knots correspond to the hierarchy of infinite primes?

    2. Further speculations

    3. The idea survives the most obvious killer test

    4. How to realize the representation of the braid hierarchy in many-sheeted space-time?



PART IV: HYPERFINITE FACTORS OF TYPE II1 AND HIERARCHY OF PLANCK CONSTANTS



HomeAbstract

    Was von Neumann Right After All?

  1. Introduction

    1. Philosophical ideas behind von Neumann algebras

    2. Von Neumann, Dirac, and Feynman

    3. Hyper-finite factors in quantum TGD

    4. Hyper-finite factors and M-matrix

    5. Connes tensor product as a realization of a finite measurement resolution

    6. Quantum spinors and fuzzy quantum mechanics

  2. Von Neumann algebras

    1. Basic definitions

    2. Basic classification of von Neumann algebras

    3. Non-commutative measure theory and non-commutative topologies and geometries

    4. Modular automorphisms

    5. Joint modular structure and sectors

    6. Basic facts about hyper-finite factors of type II

  3. Braid group, von Neumann algebras, quantum TGD, and formation of bound states

    1. Factors of von Neumann algebras

    2. Sub-factors

    3. II1 factors and the spinor structure of infinite-dimensional configuration space of 3-surfaces

    4. Space-time correlates for the hierarchy of II1 sub-factors

    5. Could binding energy spectra reflect the hierarchy of effective tensor factor dimensions?

    6. Four-color problem, II1 factors, and anyons

  4. Inclusions of II1 and III1 factors

    1. Basic findings about inclusions

    2. The fundamental construction and Temperley-Lieb algebras

    3. Connection with Dynkin diagrams

    4. Indices for the inclusions of type III1 factors

  5. TGD and hyper-finite factors of type II1: ideas and questions

    1. What kind of HFFs can one imagine in TGD?

    2. Direct sum of HFFs of type II1 as minimum option

    3. Bott periodicity, its generalization, and dimension D=8 as an inherent property of the hyper-finite II1 factor

    4. The interpretation of Jones inclusions in TGD framework

    5. Configuration space, space-time, and imbedding space and hyper-finite type II1 factors

    6. Quaternions, octonions, and hyper-finite type II1 factors

    7. Does the hierarchy of infinite primes relate to the hierarchy of II1 factors?

  6. Could HFFs of type III1 have application in TGD framework

    1. Problems associated with the physical interpretation of III1 factors

    2. Quantum measurement theory and HFFs of type III.

    3. What could one say about II1 automorphism associated with the II∞ automorphism defining factor of type III?

    4. What could be the physical interpretation of two kinds of invariants associated with HFFs type III?

    5. Does the time parameter t represent time translation or scaling?

    6. Could HFFs of type III be associated with the dynamics in M4+/- degrees of freedom?

    7. Could the continuation of braidings to homotopies involve Δit automorphisms

    8. HFFs of type III as super-structures providing additional uniqueness?

  7. The latest vision about the role of HFFs in TGD

    1. Basic facts about factors

    2. Inclusions and Connes tensor product

    3. Factors in quantum field theory and thermodynamics

    4. TGD and factors

    5. Can one identify M-matrix from physical arguments?

    6. Finite measurement resolution and HFFs

    7. Questions about quantum measurement theory in zero energy ontology

    8. How p-adic coupling constant evolution and p-adic length scale hypothesis emerge from quantum TGD proper?

    9. Some speculations related to the role of HFFs in TGD

    10. Planar algebras and generalized Feynman diagrams

    11. Miscellaneous

  8. Jones inclusions and cognitive consciousness

    1. Does one have a hierarchy of M- and U-matrices?

    2. Feynman diagrams as higher level particles and their scattering as dynamics of self consciousness

    3. Logic, beliefs, and spinor fields in the world of classical worlds

    4. Jones inclusions for hyperfinite factors of type II1 as a model for symbolic and cognitive representations

    5. Intentional comparison of beliefs by topological quantum computation?

    6. The stability of fuzzy qbits and quantum computation

    7. Fuzzy quantum logic and possible anomalies in the experimental data for the EPR-Bohm experiment

    8. Category theoretic formulation for quantum measurement theory with finite measurement resolution

  9. Appendix

    1. About inclusions of hyper-finite factors of type II1

    2. Generalization from SU(2) to arbitrary compact group



HomeAbstract

    Does TGD Predict the Spectrum of Planck Constants?

  1. Introduction

    1. The evolution of mathematical ideas

    2. The evolution of physical ideas

    3. Brief summary about the generalization of the imbedding space concept

  2. Experimental input

    1. Hints for the existence of large hbar phases

    2. Quantum coherent dark matter and hbar

    3. The phase transition changing the value of Planck constant as a transition to non-perturbative phase

  3. A generalization of the notion of imbedding space as a realization of the hierarchy of Planck constants

    1. Basic ideas

    2. The vision

    3. Hierarchy of Planck constants and the generalization of the notion of imbedding space

    4. Realization of quantum criticality in terms of number theoretic braids

    5. Realization of quantum criticality in terms of number theoretic braids

  4. Jones inclusions and generalization of the imbedding space

    1. Basic facts about Jones inclusions

    2. Jones inclusions and the hierarchy of Planck constants

    3. Questions

    4. How does the hierarchy of Planck constants affect the modified Dirac equation?

  5. Vision about dark matter as phases with non-standard value of Planck constant

    1. Dark rules

    2. Phase transitions changing Planck constant

    3. Coupling constant evolution and hierarchy of Planck constants

  6. Some applications

    1. A simple model of fractional quantum Hall effect

    2. Gravitational Bohr orbitology

    3. Accelerating periods of cosmic expansion as phase transitions increasing the value of Planck constant

    4. Phase transition changing Planck constant and expanding Earth theory

    5. Allais effect as evidence for large values of gravitational Planck constant?

    6. Applications to elementary particle physics, nuclear physics, and condensed matter physics

    7. Applications to biology and neuroscience

  7. Some mathematical speculations

    1. The content of McKay correspondence in TGD framework

    2. Jones inclusions, the large N limit of SU(N) gauge theories and AdS/CFT correspondence

    3. Could McKay correspondence and Jones inclusions relate to each other?

    4. Farey sequences, Riemann hypothesis, tangles, and TGD

    5. Only the quantum variants of M4 and M8 emerge from local hyper-finite II1 factors

  8. Appendix

    1. About inclusions of hyper-finite factors of type II1

    2. Generalization from SU(2) to arbitrary compact group



PART V: APPLICATIONS



HomeAbstract

    Cosmology and Astrophysics in Many-Sheeted Space-Time

  1. Introduction

    1. Does Equivalence Principle hold true in TGD Universe?

    2. Zero energy ontology

    3. Dark matter hierarchy and hierarchy of Planck constants

    4. Many-sheeted cosmology

    5. Cosmic strings

  2. Basic principles of General Relativity from TGD point of view

    1. General Coordinate Invariance

    2. Equivalence Principle

    3. Various interpretations of Machian Principle in TGD framework

  3. TGD inspired cosmology

    1. Robertson-Walker cosmologies

    2. Free cosmic strings

    3. Cosmic strings and cosmology

    4. Thermodynamical considerations

    5. Mechanism of accelerated expansion in TGD Universe

  4. Microscopic description of black-holes in TGD Universe

    1. Super-symplectic bosons

    2. Are ordinary black-holes replaced with super-symplectic black-holes in TGD Universe?

    3. Anyonic view about blackholes

  5. A quantum model for the formation of astrophysical structures and dark matter?

    1. TGD prediction for the parameter v0

    2. Model for planetary orbits without v0→ v0/5 scaling

    3. The interpretation of hbargr and pre-planetary period

    4. Inclinations for the planetary orbits and the quantum evolution of the planetary system

    5. Eccentricities and comets

    6. Why the quantum coherent dark matter is not visible?

    7. Quantum interpretation of gravitational Schrödinger equation

    8. How do the magnetic flux tube structures and quantum gravitational bound states relate?

    9. p-Adic length scale hypothesis and v0→ v0/5 transition at inner-outer border for planetary system

    10. About the interpretation of the parameter v0



HomeAbstract

    Elementary particle vacuum functionals

  1. Introduction

    1. First series of questions

    2. Second series of questions

    3. The notion of elementary particle vacuum functional

  2. Basic facts about Riemann surfaces

    1. Mapping class group

    2. Teichmueller parameters

    3. Hyper-ellipticity

    4. Theta functions

  3. Elementary particle vacuum functionals

    1. Extended Diff invariance and Lorentz invariance

    2. Conformal invariance

    3. Diff invariance

    4. Cluster decomposition property

    5. Finiteness requirement

    6. Stability against the decay g --> g1+g2

    7. Stability against the decay g --> g-1

    8. Continuation of the vacuum functionals to higher genus topologies

  4. Explanations for the absence of the g >2 elementary particles from spectrum

    1. Hyper-ellipticity implies the separation of g≤ 2 and g>2 sectors to separate worlds

    2. What about g> 2 vacuum functionals which do not vanish for hyper-elliptic surfaces?

    3. Should higher elementary particle families be heavy?

  5. Could also gauge bosons correspond to wormhole contacts?

    1. Option I: Only Higgs as a wormhole contact

    2. Option II: All elementary bosons as wormhole contacts

    3. Graviton and other stringy states

    4. Spectrum of non-stringy states

    5. Higgs mechanism

  6. Elementary particle vacuum functionals for dark matter

    1. Connection between Hurwitz zetas, quantum groups, and hierarchy of Planck constants?

    2. Hurwitz zetas and dark matter



HomeAbstract

    Massless States and Particle Massivation

  1. Introduction

    1. How p-adic coupling constant evolution and p-adic length scale hypothesis emerge from quantum TGD?

    2. Physical states as representations of super-symplectic and Super Kac-Moody algebras

    3. Particle massivation

    4. Topics of the chapter

  2. Identification of elementary particles and the role of Higgs in particle massivation

    1. Identification of elementary particles

    2. New view about the role of Higgs boson in massivation

    3. General mass formulas

  3. Number theoretic compactification and M8-H duality

    1. Basic idea behind M8-M4× CP2 duality

    2. Minimal form of M8-H duality

    3. Strong form of M8-H duality

    4. M8-H duality and low energy hadron physics

    5. The notion of number theoretic braid

    6. Connection with string model and Equivalence Principle at space-time level

  4. Does the modified Dirac action define the fundamental action principle?

    1. Modified Dirac equation

    2. Quantum criticality and modified Dirac equation

    3. Handful of problems with a common resolution

  5. Representations for the configuration space γ matrices in terms of super-symplectic charges at light cone boundary

    1. Magnetic flux representation of the super-symplectic algebra

    2. Quantization of the modified Dirac action

    3. Expressions for super-symplectic generators in finite measurement resolution

  6. Super-symmetries at space-time and configuration space level

    1. Configuration space as a union of symmetric spaces

    2. Isometries of configuration space as symplectic transformations of δ M4+/-× CP2

    3. SUSY algebra defined by the anticommutation relations of fermionic oscillator operators and WCW local Clifford algebra elements as chiral super-fields

    4. Identification of Kac-Moody symmetries

    5. Coset space structure for configuration space as symmetric space

    6. Comparison of TGD and string views about super-conformal symmetries

  7. Color degrees of freedom

    1. SKM algebra

    2. General construction of solutions of Dirac operator of H

    3. Solutions of the leptonic spinor Laplacian

    4. Quark spectrum

  8. Exotic states

    1. What kind of exotic states one expects?

    2. Are S2 degrees of freedom frozen for elementary particles?

    3. More detailed considerations

  9. Particle massivation

    1. Partition functions are not changed

    2. Fundamental length and mass scales

    3. Spectrum of elementary particles

    4. Can p-adic thermodynamics explain the masses of intermediate gauge bosons?

    5. Probabilistic considerations

  10. Modular contribution to the mass squared

    1. The physical origin of the genus dependent contribution to the mass squared

    2. Generalization of Theta functions and quantization of p-adic moduli

    3. The calculation of the modular contribution Δ h to the conformal weight



Home

    Appendix

  1. Basic properties of CP2

    1. CP2 as a manifold

    2. Metric and Kähler structures of CP2

    3. Spinors in CP2

    4. Geodesic sub-manifolds of CP2

  2. CP2 geometry and standard model symmetries

    1. Identification of the electro-weak couplings

    2. Discrete symmetries

  3. Basic facts about induced gauge fields

    1. Induced gauge fields for space-times for which CP2 projection is a geodesic sphere

    2. Space-time surfaces with vanishing em, Z0, or Kähler fields

  4. p-Adic numbers and TGD

    1. p-Adic number fields

    2. Canonical correspondence between p-adic and real numbers



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