I am grateful for comments, criticism and suggestions. The following list gives table of contents for "Quantum TGD". 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.



TOWARDS M-MATRIX



||Introduction||
PART I: GENERAL THEORY
||Basic Extremals of the Kähler action||Construction of Quantum Theory: Symmetries||Construction of Quantum Theory: M-matrix||Category Theory and Quantum TGD|| Twistors, N=4 Super-Conformal Symmetry, and Quantum TGD|| Quantum Field Theory Limit of TGD from Bosonic Emergence|| Does the QFT Limit of TGD Have Space-Time Super-Symmetry?||Coupling Constant Evolution in Quantum TGD ||
PART II: HYPER-FINITE FACTORS AND HIERARCHY OF PLANCK CONSTANTS
|| Was von Neumann Right After All||Does TGD Predict the Spectrum of Planck Constants?||Quantum Hall effect and Hierarchy of Planck Constants||
APPENDICES
||Appendix A: Quantum Groups and Related Structures||Appendix B||



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 of consciousness

    4. TGD as a generalized number theory

    5. Dynamical quantized Planck constant and dark matter hierarchy

  3. The contents of the book

    1. Part I: General Theory

    2. Part II: Hyper-Finite Factors of Type II and Hierarchy of Planck Constants

    3. Part III: Miscellaneous Material Out of Date



PART I: GENERAL THEORY



HomeAbstract

    Basic extremals of the Kähler action

  1. Introduction

    1. In what sense field equations could mimic dissipative dynamics?

    2. The dimension of CP2 projection as a classified for the fundamental phases of matter

    3. Basic extremals of Kähler action

    4. Weak form of electric magnetic duality and modification of Kähler action

  2. General considerations

    1. Number theoretical compactification and M8-H duality

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

    4. Can one determine experimentally the shape of the space-time surface?

  3. 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

  4. Vacuum extremals

    1. CP2 type extremals

    2. Vacuum extremals with vanishing induced Kähler field

  5. Non-vacuum extremals

    1. Cosmic strings

    2. Massless extremals

    3. Generalization of the solution ansatz defining massless extremals

    4. Maxwell phase

    5. Stationary, spherically symmetric extremals

    6. Maxwell hydrodynamics as a toy model for TGD

  6. Weak form of electric-magnetic duality and its implications

    1. Could a weak form of electric-magnetic duality hold true?

    2. Magnetic confinement, the short range of weak forces, and color confinement

    3. Should J+J1 appear in Kähler action?

    4. Could Quantum TGD reduce to almost topological QFT?

    5. A general solution ansatz to field equations for J+J1 option

    6. Hydrodynamical picture in the fermionic sector

  7. How to define Dirac determinant?

    1. Dirac determinant when the number of eigenvalues is infinite

    2. Hyper-octonionic primes

    3. The three basic options for the pseudo-momentum spectrum



HomeAbstract

    Construction of Quantum Theory: Symmetries

  1. Introduction

    1. Physics as infinite-dimensional geometry

    2. p-Adic physics as physics of cognition and intentionality

    3. Hierarchy of Planck constants and dark matter hierarchy

    4. Number theoretical symmetries

  2. Symmetries

    1. General Coordinate Invariance and generalized quantum gravitational holography

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

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

    4. Symplectic transformations of δ M4+/-× CP2 as isometries of configuration space

    5. Does the symmetric space property reduce to coset construction for Super Virasoro algebras?

    6. What effective 2-dimensionality and holography really mean?

    7. About the relationship between super-symplectic and super Kac-Moody algebras

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

  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

    4. Generalized eigenvalues of DC-S and General Coordinate Invariance

  5. 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

  6. Trying to understand N=4 super-conformal symmetry

    1. Large N=4 SCA

    2. Overall view about how different N=4 SCAs could emerge in TGD framework

    3. How large N=4 SCA could emerge in TGD?

    4. Relationship to super-string models, M theory, and WZW model

    5. The interpretation of the critical dimension D=4 and the objection related to the signature of the space-time metric

    6. How could exotic Kac-Moody algebras emerge from Jones inclusions?

    7. Are both quark and lepton like chiralities needed/possible?

  7. Generalization of the notion of imbedding space

    1. Generalization of the notion of imbedding space

    2. Phase transitions changing the value of Planck constant

    3. Could the dynamics of Kähler action predict the hierarchy of Planck constants?

  8. Could a symplectic analog of conformal field theory be relevant for quantum TGD?

    1. Symplectic QFT at sphere

    2. Symplectic QFT with spontaneous breaking of rotational and reflection symmetries

    3. Generalization to quantum TGD



HomeAbstract

    Construction of Quantum Theory: M-matrix

  1. Introduction

    1. The recent progress in Quantum TGD and identification of M-matrix

    2. Various inputs to the construction of M-matrix

    3. Topics of the chapter

  2. Basic philosophical ideas

    1. Zero energy ontology

    2. The anatomy of the quantum jump

  3. Zero energy ontology and conformal invariance

    1. M-matrix as characterizer of time-like entanglement between positive and negative energy components of zero energy state

    2. Feynman rules in configuration space degrees of freedom

    3. Rational conformal field theories and stringy scattering amplitudes

    4. Issues related to Lorentz symmetry

  4. Weak form of electric-magnetic duality and fermionic propagator

    1. Could Quantum TGD reduce to almost topological QFT?

    2. A general solution ansatz to field equations for J+J1 option

    3. Hydrodynamical picture in the fermionic sector

    4. Hyper-octonionic primes

    5. The three basic options for the pseudo-momentum spectrum

  5. How to define Feynman diagrams?

    1. Questions

    2. Generalized Feynman diagrams at fermionic and momentum space level

    3. Harmonic analysis in WCW as a manner to calculate WCW functional integrals

  6. 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

  7. Number theoretic criticality and M-matrix

    1. Number theoretic constraints on M-matrix

    2. M-matrix and the notion of number theoretic braid

    3. Physical representations of Galois groups

  8. Are both symplectic and conformal field theories needed?

    1. Symplectic QFT at sphere

    2. Symplectic QFT with spontaneous breaking of rotational and reflection symmetries

    3. Generalization to quantum TGD

  9. What can one say about the braiding part of M-matrix?

    1. Are factorizable QFT in M2 and topological QFT in S2 associated with quantum criticality?

    2. Factorizing 2-D S-matrices and scattering at quantum criticality

    3. Are unitarity and Lorentz invariance consistent for the quantum critical M-matrix constructed from factorizing S-matrices?

  10. What can one say about U-matrix?

    1. U-matrix as a tensor product of S-matrix part of M-matrix and its Hermitian conjugate?

    2. The unitarity conditions of U-matrix for HFFs of type II1?

    3. U-matrix can have elements between different number fields

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



HomeAbstract

    Category Theory and Quantum TGD

    1. Introduction

    2. S-matrix as a functor

      1. The *-category of Hilbert spaces

      2. The monoidal *-category of Hilbert spaces and its counterpart at the level of nCob

      3. TQFT as a functor

      4. The situation is in TGD framework

    3. Some general ideas

      1. Operads, number theoretical braids, and inclusions of HFFs

      2. Generalized Feynman diagram as category?

    4. Planar operads, the notion of finite measurement resolution, and arrow of geometric time

      1. Zeroth order heuristics about zero energy states

      2. Planar operads

      3. Planar operads and zero energy states

      4. Relationship to ordinary Feynman diagrammatics

    5. Category theory and symplectic QFT

      1. Fusion rules

      2. Symplectic diagrams

      3. A couple of questions inspired by the analogy with conformal field theories

      4. Associativity conditions and braiding

      5. Finite-dimensional version of the fusion algebra

    6. Could operads allow the formulation of the generalized Feynman rules?

      1. How to combine conformal fields with symplectic fields?

      2. Symplecto-conformal fields in Super Kac-Moody sector

      3. The treatment of four-momentum

      4. What does the improvement of measurement resolution really mean?

      5. How do the operads formed by generalized Feynman diagrams and symplecto-conformal fields relate?

    7. Possible other applications of category theory

      1. Inclusions of HFFs and planar tangles

      2. 2-plectic structures and TGD

      3. TGD variant for the category nCob

      4. Number theoretical universality and category theory

      5. Category theory and fermionic parts of zero energy states as logical deductions

      6. Category theory and hierarchy of Planck constants



HomeAbstract

    Twistors, N=4 Super-Conformal Symmetry, and Quantum TGD

  1. Introduction

    1. Twistors and classical TGD

    2. Twistors and Feynman diagrams

    3. Twistors and electric-magnetic duality

  2. Could the target space be identified in terms of twistors?

    1. General remarks

    2. What twistor Fourier transform could mean in TGD framework?

    3. Could one define the phase factor of the twistor uniquely?

  3. Could one regard space-time surfaces as surfaces in twistor space?

    1. How M4× CP2 emerges in twistor context?

    2. How to identify twistorial surfaces in PT× CP2 and how to map them to M4× CP2?

    3. How to code the basic parameters of preferred extremals in terms of twistors?

    4. Hyper-quaternionic and co-hyper-quaternionic surfaces and twistor duality

  4. Could one lift Feynman diagrams to twistor space?

    1. The treatment of massive case in terms of twistors

    2. Purely twistorial formulation of Feynman graphs

    3. What could be the propagator in twistor space?

    4. What to do with the perturbation theory?

  5. 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?

  6. The simplest vision about how twistors might emerge from TGD

    1. Generalized eigen modes for the modified Chern-Simons Dirac equation and hydrodynamical picture

    2. Generalized Feynman diagrams at fermionic and momentum space level

    3. Hyper-octonionic primes

    4. Generalized Feynman diagrams at fermionic and momentum space level

    5. Three basic options for the pseudo-momentum spectrum

  7. What could be the generalization of Yangian symmetry of N=4 SUSY in TGD framework?

    1. Background

    2. Yangian symmetry

    3. How to generalize Yangian symmetry in TGD framework?

    4. Is there any hope about description in terms of Grassmannians?

    5. Could zero energy ontology make possible full Yangian symmetry?

    6. Could Yangian symmetry provide a new view about conserved quantum numbers?

    7. What about the selection of preferred M2 subset M4

    8. Does M8-H duality generalize the duality between twistor and momentum twistor descriptions?



HomeAbstract

    Quantum Field Theory Limit of TGD from Bosonic Emergence

  1. Introduction

    1. The dream

    2. Improved dream

    3. SUSY improved dream

    4. ZEO improved dream

    5. What can one conclude?

  2. Bootstrap approach to obtain a unitary S-matrix

    1. Quantitative realization of UV finiteness in terms of p-adic length scale hypothesis and finite measurement resolution

    2. A more detailed summary of Feynman diagrammatics

    3. Could quantum criticality fix hyperbolic cutoff uniquely?

  3. Calculation of the bosonic propagator

    1. The basic integrals

    2. How to avoid generation of mass term?

    3. Explicit form of the integrals

    4. k-integration for the principal value parts of the integrals

    5. Numerical calculation of the integrals over the hyperbolic angle

  4. How quantum criticality could predict the evolution of hyperbolic cutoff?

    1. Summary about how ideas about quantum criticality have evolved

    2. Searching for the solutions of criticality conditions

    3. Could p-adic fractality solve the problems?

  5. Further progress

    1. Could supersymmetry make momentum cutoffs un-necessary?

    2. Generalized Feynman diagrams at fermionic and momentum space level



HomeAbstract

    Does the QFT Limit of TGD Have Space-Time Super-Symmetry?

  1. Introduction

  2. SUSY briefly

    1. Weyl fermions

    2. SUSY algebras

    3. Super-space

    4. Non-renormalization theorems

  3. Does TGD allow the counterpart of space-time super-symmetry?

    1. Basic data bits

    2. Could one generalize super-symmetry?

    3. Modified Dirac equation briefly

    4. TGD counterpart of space-time super-symmetry

    5. Experimental indication for space-time super-symmetry

  4. Octo-twistors 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?

  5. SUSY algebra of fermionic oscillator operators and WCW local Clifford algebra elements as super-fields

    1. Super-algebra associated with the modified gamma matrices

    2. Super-fields associated with WCW Clifford algebra

  6. SUSY algebra at QFT limit

    1. Minimum information about space-time sheet and particle quantum numbers needed to formulate SUSY algebra

    2. The physical picture behind the realization of SUSY algebra at point like limit

    3. Explicit form of the SUSY algebra at QFT limit

    4. How the representations of SUSY in TGD differ from the standard representations?

  7. Super-symmetric QFT limit of TGD

    1. Basic concepts and ideas

    2. About super-field formalism in N=2 case

    3. Electric magnetic duality, monopole condensation and confinement from TGD point view

    4. Interpretation of Kähler potential and super-potential terms in TGD framework

    5. Generalization of bosonic emergence

    6. Is N> 8 supersymmetry internally consistent?

    7. Super fields in TGD framework

    8. Could QFT limit be finite?

    9. Can one understand p-adic coupling constant evolution as a prediction of QFT limit?

    10. Is the QFT type description of gravitational interactions possible?

  8. A more detailed summary of Feynman diagrammatics

  9. Emergence in absence of super-symmetry

  10. Some differences from standard Feynman diagrammatics

  11. Generalization of the formalism to the super-symmetric case



HomeAbstract

    Coupling Constant Evolution in Quantum TGD

  1. Introduction

    1. Geometric ideas

    2. The construction of S-matrix

    3. Vision about coupling constant evolution

  2. Basic conceptual framework

    1. Basic concepts

    2. Gauge charges and gauge fluxes

    3. Can one regard # resp #B contacts as particles resp string like objects?

    4. TGD based description of external fields

    5. Number theoretical considerations

  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. Microscopic identification of Weinberg angle

  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. The notion of number theoretical braid

  5. General vision about real and p-adic coupling constant evolution

    1. A general view about coupling constant evolution

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

  6. Weak form of electric-magnetic duality and its implications

    1. Could a weak form of electric-magnetic duality hold true?

    2. Magnetic confinement, the short range of weak forces, and color confinement

    3. Should J+J1 appear in Kähler action?

    4. Could Quantum TGD reduce to almost topological QFT?

  7. How to define Feynman diagrams?

    1. Questions

    2. Generalized Feynman diagrams at fermionic and momentum space level

    3. How to define integration and p-adic Fourier analysis and p-adic counterparts of geometric objects?

    4. Harmonic analysis in WCW as a manner to calculate WCW functional integrals

  8. Does the evolution of gravitational coupling make sense at space-time level?

    1. Is stringy action principle coded by the geometry of preferred extremals?

    2. What does the equality of gravitational and inertial masses mean?

    3. What about induced spinor fields at stringy curves?

    4. What is the connection with General Relativity?

    5. What does one mean with the evolution of gravitational constant?

  9. RG invariance of gauge couplings inside CD

    1. Are all gauge couplings RG invariants within given CD?

    2. Slicing of space-time surface by light-like 3-surfaces

    3. Coupling constant evolution as evolution of classical gauge fluxes

    4. Questions related to the physical interpretation

  10. Quantitative predictions for the values of coupling constants

    1. A revised view about coupling constant evolution

    2. Why gravitation is so weak as compared to gauge interactions?

  11. p-Adic coupling constant evolution

    1. p-Adic coupling constant evolution associated with length scale resolution at space-time level

    2. p-Adic evolution in angular resolution and dynamical Planck constant

    3. Large values of Planck constant and electro-weak and strong coupling constant evolution

    4. Super-canonical gluons and non-perturbative aspects of hadron physics

    5. Why Mersenne primes should label a fractal hierarchy of physics?

    6. The formula for the hadronic string tension

    7. How p-adic and real coupling constant evolutions are related to each other?

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

  12. Appendix A: Identification of the electro-weak couplings

  13. Appendix B: Some number theoretical conjectures related to p-adicization

    1. Fusion of p-adic and real physics to single coherent whole by algebraic continuation

    2. The number theoretical universality of Riemann Zeta

    3. Some wrong number theoretical conjectures




PART II: HYPER-FINITE FACTORS 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



HomeAbstract

    Quantum Hall effect and Hierarchy of Planck Constants

  1. Introduction

  2. About theories of quantum Hall effect

    1. Quantum Hall effect as a spontaneous symmetry breaking down to a discrete subgroup of the gauge group

    2. Witten-Chern-Simons action and topological quantum field theories

    3. Chern-Simons action for anyons

    4. Topological quantum computation using braids and anyons

  3. 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. Could the dynamics of Kähler action predict the hierrchy of Planck constants?

  4. Weak form of electric-magnetic duality and its implications

    1. Could a weak form of electric-magnetic duality hold true?

    2. Magnetic confinement, the short range of weak forces, and color confinement

    3. Should J+J1 appear in Kähler action?

    4. Could Quantum TGD reduce to almost topological QFT?

    5. A general solution ansatz to field equations for J+J1 option

    6. Hydrodynamical picture in the fermionic sector

  5. How to define Dirac determinant?

    1. Dirac determinant when the number of eigenvalues is infinite

    2. Hyper-octonionic primes

    3. The three basic options for the pseudo-momentum spectrum

  6. Quantum Hall effect, charge fractionization, and hierarchy of Planck constants

    1. Quantum Hall effect

    2. A simple model for fractional quantum Hall effect

    3. Could QHE described in terms of "gauge part" of Kähler gauge potential

    4. Constraints on the Kähler structure of generalized imbedding space from charge fractionization

    5. In what kind of situations do anyons emerge?

    6. What happens in QHE?



APPENDICES



Home

    Appendix A: Quantum Groups and Related Structures

  1. Introduction

  2. Hopf algebras and ribbon categories as basic structures

    1. Hopf algebras and ribbon categories very briefly

    2. Algebras, co-algebras, bi-algebras, and related structures

    3. Tensor categories

  3. Axiomatic approach to S-matrix based on the notion of quantum category

    1. Δ andμand the axioms eliminating loops

    2. The physical interpretation of non-trivial braiding and quasi-associativity

    3. Generalizing the notion of bi-algebra structures at the level of configuration space

    4. Ribbon category as a fundamental structure?

    5. Minimal models and TGD

  4. Some examples of bi-algebras and quantum groups

    1. Simplest bi-algebras

    2. Quantum group Uq(sl(2))

    3. General semisimple quantum group

    4. Quantum affine algebras



Home

    Appendix B:

  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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