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: THE RECENT VIEW ABOUT FIELD EQUATIONS
||Basic Extremals of Kähler action||About Identification of the Preferred extremals of Kähler Action||WCW Spinor Structure||Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds"||Can one apply Occam's razor as a general purpose debunking argument to TGD?||
PART II: GENERAL THEORY
||Construction of Quantum Theory: Symmetries||Zero Energy Ontology and M-matrix||What Scattering Amplitudes Should Look Like?|| Does Riemann Zeta Code for Generic Coupling Constant Evolution?|| Could N=2 Super-Conformal Algebra Be Relevant For TGD?||
PART III: TWISTORS AND TGD
TGD Variant of Twistor Story|| From Principles to Diagrams|| How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD?|| Some Questions Related to the Twistor Lift of TGD?||
PART IV: CATEGORIES AND TGD
Category Theory and Quantum TGD|| Could categories, tensor networks, and Yangians provide the tools for handling the complexity of TGD? || Are higher structures needed in the categorification of TGD? ||Is Non-Associative Physics and Language Possible Only in Many-Sheeted Space-Time? ||
PART V: MISCELLANEOUS TOPICS
Does the QFT Limit of TGD Have Space-Time Super-Symmetry?|| Coupling Constant Evolution in Quantum TGD||



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: The Recent View about Field Equations

    2. Part II: General Theory

    3. Part III: Twistors and TGD

    4. Part IV: Categories and TGD

    5. Part V: Miscellaneous topics



PART I: THE RECENT VIEW ABOUT FIELD EQUATIONS



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

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

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

  3. The vanishing of super-conformal charges as a gauge conditions selecting preferred extremals of Kähler action

    1. Field equations for Kähler action

    2. Boundary conditions at boundaries of CD

    3. Boundary conditions at parton orbits

  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. Vacuum extremals

    1. CP2 type extremals

    2. Vacuum extremals with vanishing induced Kähler field

  6. 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



HomeAbstract

    About Identification of the preferred extremals of Kähler action

  1. Introduction

    1. Preferred extremals as critical extremals

    2. Construction of preferred extremals

  2. Weak form 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. Could Quantum TGD reduce to almost topological QFT?

  3. Some attempts to understand preferred extremals of Kähler action

    1. What "preferred" could mean?

    2. Basic ideas about preferred extremals

    3. What could be the construction recipe for the preferred extremals assuming CP_2= CP_2^{mod

    4. Are Euclidian regions of preferred extremals quaternion-Kähler manifolds?

    5. Could quaternion analyticity make sense for the preferred extremals?

  4. In what sense TGD could be an integrable theory?

    1. What integrable theories are?

    2. Why TGD could be integrable theory in some sense?

    3. Could TGD be an integrable theory?

  5. Do geometric invariants of preferred extremals define topological invariants of space-time surface and code for quantum physics?

    1. Preferred extremals of Kähler action as manifolds with constant Ricci scalar whose geometric invariants are topological invariants

    2. Is there a connection between preferred extremals and AdS_4/CFT correspondence?

    3. Generalizing Ricci flow to Maxwell flow for 4-geometries and Kähler flow for space-time surfaces

    4. Could correlation functions, S-matrix, and coupling constant evolution be coded the statistical properties of preferred extremals?

  6. About deformations of known extremals of Kähler action

    1. What might be the common features of the deformations of known extremals

    2. What small deformations of CP2 type vacuum extremals could be?

    3. Hamilton-Jacobi conditions in Minkowskian signature

    4. Deformations of cosmic strings

    5. Deformations of vacuum extremals?

    6. About the interpretation of the generalized conformal algebras

  7. Appendix: Hamilton-Jacobi structure

    1. Hermitian and hyper-Hermitian structures

    2. Hamilton-Jacobi structure



Home Abstract

    WCW Spinor Structure

  1. Introduction

    1. Basic principles

    2. Kähler-Dirac action

  2. WCW spinor structure: general definition

    1. Defining relations for gamma matrices

    2. General vielbein representations

    3. Inner product for WCW spinor fields

    4. Holonomy group of the vielbein connection

    5. Realization of WCW gamma matrices in terms of super symmetry generators

    6. Central extension as symplectic extension at configuration space level

    7. WCW Clifford algebra as a hyper-finite factor of type II_1

  3. Under what conditions electric charge is conserved for the modified Dirac equation?

    1. Conservation of em charge for Kähler Dirac equation

    2. About the solutions of Kähler Dirac equation for known extremals

    3. Concrete realization of the conditions guaranteeing well-defined em charge

    4. Connection with number theoretic vision?

  4. Representation of WCW metric as anti-commutators of gamma matrices identified as symplectic super-charges

    1. Expression for WCW Kähler metric as anticommutators as symplectic super charges

    2. Handful of problems with a common resolution

    3. Overall view about Kähler action and Kähler Dirac action

    4. Radon, Penrose ja TGD

  5. Quantum criticality and Kähler-Dirac action

    1. What quantum criticality could mean?

    2. Quantum criticality and fermionic representation of conserved charges associated with second variations of Kähler action

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

    4. Quantum criticality and electroweak symmetries

    5. The emergence of Yangian symmetry and gauge potentials as duals of Kac-Moody currents

  6. Kähler-Dirac equation and super-symmetries

    1. Super-conformal symmetries

    2. WCW geometry and super-conformal symmetries

    3. The relationship between inertial gravitational masses

    4. Realization of space-time SUSY in TGD

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

  7. Still about induced spinor fields and TGD counterpart for Higgs

    1. More precise view about modified Dirac equation

    2. A more detailed view about string world sheets

    3. Classical Higgs field again



Home Abstract

    Recent View about Kähler Geometry and Spin Structure of "World of Classical Worlds"

  1. Introduction

  2. WCW as a union of homogenous or symmetric spaces

    1. Basic vision

    2. Equivalence Principle and WCW

    3. EP at quantum and classical level

    4. Criticism of the earlier construction

    5. Is WCW homogenous or symmetric space?

    6. Symplectic and Kac-Moody algebras as basic building bricks

  3. Updated view about Kähler geometry of WCW

    1. Kähler function, Kähler action, and connection with string models

    2. Realization of super-conformal symmetries

    3. Classical number fields and associativity and commutativity as fundamental law of physics

  4. About some unclear issues of TGD

    1. Adelic vision and symmetries

    2. Quantum-classical correspondence for fermions

    3. Strong form of holography for fermions

    4. The relationship between spinors in space-time interior and at boundaries between Euclidian and Minkoskian regions

    5. About second quantization of the induced spinor fields

    6. Is statistical entanglement "real"?

  5. About the notion of four-momentum in TGD framework

    1. Scale dependent notion of four-momentum in zero energy ontology

    2. Are the classical and quantal four-momenta identical?

    3. What Equivalence Principle (EP) means in quantum TGD?

    4. TGD-GRT correspondence and Equivalence Principle

    5. How translations are represented at the level of WCW?

    6. Yangian and four-momentum

  6. Generalization of AdS/CFT duality to TGD framework

    1. Does the exponent of Chern-Simons action reduce to the exponent of the area of minimal surfaces?

    2. Does Kähler action reduce to the sum of areas of minimal surfaces in effective metric?

    3. Surface area as geometric representation of entanglement entropy?

    4. Related ideas

    5. The importance of being light-like

  7. Could one define dynamical homotopy groups in WCW?

    1. About cobordism as a concept

    2. Prastaro's generalization of cobordism concept to the level of partial differential equations

    3. Why Prastaro's idea resonates so strongly with TGD

    4. What preferred extremals are?

    5. Could dynamical homotopy/homology groups characterize WCW topology?

    6. Appendix: About field equations of TGD in jet bundle formulation



HomeAbstract

    Can one apply Occam's razor as a general purpose debunking argument to TGD?

  1. Introduction

  2. Simplicity at various levels

    1. WCW level: a generalization of Einstein's geometrization program to entire quantum physics

    2. Space-time level: many-sheeted space-time and emergence of classical fields and GRT space-time

    3. Imbedding space level

  3. Some questions about TGD

    1. In what aspects TGD extends other theory/theories of physics?

    2. In what sense TGD is simplification/extension of existing theory?

    3. What is the hypothetical applicability of the extension - in energies, sizes, masses etc?

    4. What is the leading correction/contribution to physical effects due to TGD onto particles, interactions, gravitation, cosmology?



PART II: GENERAL THEORY



HomeAbstract

    Construction of Quantum Theory: Symmetries

  1. Introduction

    1. Physics as infinite-dimensional Kähler 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 WCW

    4. Symplectic transformations of δM4+/-× CP2 as isometries of WCW

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

    6. Symplectic and Kac-Moody algebras as basic building bricks

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

  3. WCW as a union of homogenous or symmetric spaces

    1. Basic vision

    2. Equivalence Principle and WCW

    3. EP at quantum and classical level

    4. Criticism of the earlier construction

    5. Is WCW homogenous or symmetric space?

    6. Symplectic and Kac-Moody algebras as basic building bricks

    7. WCW as a union of symmetric spaces

    8. Isometries of WCW geometry as symplectic transformations of δM4+/-× CP2

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

    10. Identification of Kac-Moody symmetries

    11. Coset space structure for WCW as a symmetric space

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

  4. 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



HomeAbstract

    Zero Energy Ontology and Matrices

  1. Introduction

    1. Zero energy ontology and interpretation of light-like 3-surfaces as generalized Feynman diagrams

    2. Identification of the counterpart of M-matrix as time-like entanglement coefficients

    3. Topics of the chapter

  2. Zero energy ontology

    1. Motivations for zero energy ontology

    2. Zero energy ontology

    3. The anatomy of quantum jump in zero energy ontology (ZEO)

    4. Conscious entities and arrow of time in TGD Universe

  3. A vision about the role of HFFs in TGD

    1. Basic facts about factors

    2. Factors in quantum field theory and thermodynamics

    3. TGD and factors

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

    5. Finite measurement resolution and HFFs

    6. Questions about quantum measurement theory in zero energy ontology

    7. Miscellaneous

  4. The relation between U-matrix and M-matrices

    1. What one can say about M-matrices?

    2. How does the size scale of CD affect M-matrices?

    3. What can one say about $U$-matrix?

    4. How to obtain unitarity correctly?

    5. What about the identification of $S$?

    6. What about quantum classical correspondence?



HomeAbstract

    What Scattering Amplitudes Should Look Like?

  1. Introduction

  2. General vision behind matrices

    1. Basic principles

    2. Various inputs to the construction of M-matrix

    3. But what about the concrete Feynman rules?

  3. Scattering amplitudes at the level of WCW

    1. Questions

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

  4. A more detailed view about the construction of scattering amplitudes

    1. Basic principles

    2. Elementary particles in TGD framework

    3. Scattering amplitudes

    4. What one should obtain at QFT limit?

    5. What is the relationship of generalized Feynman diagrams to twistor diagrams?

    6. Generalized twistor diagrams and planar operads



PART III: TWISTORS AND TGD



HomeAbstract

    TGD variant of the twistor story

  1. Introduction

  2. Background and motivations

    1. Basic results and problems of twistor approach

    2. Results about twistors relevant for TGD

    3. Basic definitions related to twistor spaces

    4. Why twistor spaces with Kähler structure?

  3. About the identification of 6-D twistor spaces as sub-manifolds of CP3× F3

    1. Conditions for twistor spaces as sub-manifolds

    2. Twistor spaces by adding CP1 fiber to space-time surfaces

    3. Twistor spaces as analogs of Calabi-Yau spaces of super string models

    4. Are Euclidian regions of preferred extremals quaternion-Kähler manifolds?

    5. Could quaternion analyticity make sense for the preferred extremals?

  4. Witten's twistor string approach and TGD

    1. Basic ideas about twistorialization of TGD

    2. The emergence of the fundamental 4-fermion vertex and of boson exchanges

    3. What about SUSY in TGD?

    4. What does one really mean with the induction of imbedding space spinors?

    5. About the twistorial description of light-likeness in 8-D sense using octonionic spinors

    6. How to generalize Witten's twistor string theory to TGD framework?

    7. Yangian symmetry

    8. Does BCFW recursion have counterpart in TGD?

    9. Possible connections of TGD approach with the twistor Grassmannian approach

    10. Permutations, braidings, and amplitudes

  5. Could the Universe be doing Yangian arithmetics?

    1. Do scattering amplitudes represent quantal algebraic manipulations?

    2. Generalized Feynman diagram as shortest possible algebraic manipulation connecting initial and final algebraic objects

    3. This was not the whole story yet

  6. From Principles To Diagrams

    1. Some mathematical background

    2. Surprise: twistorial dynamics does not reduce to a trivial reformulation of the dynamics of Kähler action

    3. Basic principles behind construction of amplitudes

  7. Some mathematical details about Grasmannian formalism

    1. Yangian algebra and its super counterpart

    2. Twistors and momentum twistors and super-symmetrization

    3. Brief summary of the work of Arkani-Hamed and collaborators

    4. The general form of Grassmannian integrals

    5. Canonical operations for Yangian invariants

    6. Explicit formulation for recursion relation



HomeAbstract

    From Principles to Diagrams

  1. Introduction

  2. Twistorial lift of Kähler action

    1. Imbedding space is twistorially unique

    2. Some basic definitions

    3. What does twistor structure in Minkowskian signature really mean?

    4. What does the induction of the twistor structure to space-time surface really mean?

    5. Could M4 Kähler form introduce new gravitational physics?

    6. A connection with the hierarchy of Planck constants?

    7. Twistorial variant for the imbedding space spinor structure

    8. Twistor googly problem transforms from a curse to blessing in TGD framework

  3. Surprise: twistorial dynamics does not reduce to a trivial reformulation of the dynamics of Kähler action

    1. New scales emerge

    2. Estimate for the cosmic evolution of RD

    3. What about extremals of the dimensionally reduced 6-D Kähler action?

  4. How the hierarchy of Planck constants might relate to the almost vacuum degeneracy for twistor lift of TGD?

    1. Twistor lift of TGD

    2. Hierarchy of Planck constants

    3. Magnetic flux tubes as mediators of interactions

    4. Quantum criticality condition

    5. Is inflation theory simply wrong?

  5. Basic principles behind construction of amplitudes

    1. Imbedding space is twistorially unique

    2. Strong form of holography

    3. The existence of WCW demands maximal symmetries

    4. Quantum criticality

    5. Physics as generalized number theory, number theoretical universality

    6. Scattering diagrams as computations

    7. Reduction of diagrams with loops to braided tree-diagrams

    8. Scattering amplitudes as generalized braid invariants

  6. Tensor Networks and S-matrices

    1. Twistorial and number theoretic visions

    2. Generalization of the notion of unitarity

    3. Scattering diagrams as tensor networks constructed from perfect tensors

    4. Eigenstates of Yangian co-algebra generators as a manner to generate maximal entanglement?

    5. Two different tensor network descriptions

    6. Taking into account braiding and WCW degrees of freedom

    7. How do the gauge couplings appear in the vertices?



HomeAbstract

    About twistor lift of TGD?

  1. Introduction

  2. More about twistor lift of Kähler action

    1. Kähler action contains overall scale as a hidden coupling parameter

    2. The problem with cosmological constant

  3. Twistor lift of TGD, hierarchy of Planck constant, quantum criticality, and p-adic length scale hypothesis

    1. Twistor lift brings volume term back

    2. ZEO and twistor lift

    3. Hierarchy of Planck constants

    4. Magnetic flux tubes as mediators of interactions

    5. Two variants for p-adic length scale hypothesis for cosmological constant

  4. What happens for the extremals of Kähler action in twistor lift

    1. The coupling between Kähler action and volume term

    2. Twistor lift and the extremals of Kähler action

    3. Are minimal surface extremals of Kähler action holomorphic surfaces in some sense?

  5. About string like objects

    1. Two options for fundamental variational principle

    2. How to achieve low value of string tension?

    3. How does the gravitational coupling emerge?

    4. Non-commutative imbedding space and strong form of holography



HomeAbstract

    Some Questions Related to the Twistor Lift of TGD

  1. Introduction

    1. Questions related to the classical aspects of twistorialization

    2. Questions related to the quantum aspects of twistorialization

  2. More details about the induction of twistor structure

    1. What does one mean with twistor space?

    2. Twistor lift of TGD

    3. Solutions to the conditions defining the twistor lift

    4. Twistor lift and the reduction of field equations and SH to holomorphy

  3. How does the twistorialization at imbedding space level emerge?

    1. M8-H duality at space-time level

    2. Parametrization of light-like quaternionic 8-momenta in terms of T(CP2)

    3. A new view about color, color confinement, and twistors

    4. How do the two twistor spaces assignable to M^4 relate to each other?

    5. Can the Kähler form of M4 appear in Kähler action?

    6. What causes CP violation?

  4. About the interpretation of the duality assignable to Yangian symmetry

    1. Formal definition associated with Yangian

    2. Dual conformal symmetry in N=4 SUSY

    3. Possible TGD based interpretation of Yangian symmetries

    4. Is there a duality between associative and co-associative space-time surfaces?

  5. TGD view about construction of twistor amplitudes

    1. Some key ideas of the twistor Grassmann approach

    2. Basic vision behind scattering amplitudes

    3. Options for the construction of scattering amplitudes

    4. About problems related to the construction of twistor amplitudes

  6. Appendix: Some background about twistors

    1. The pioneering works of Penrose and Witten

    2. BCFW recursion formula

    3. Yangian symmetry and Grassmannian

    4. Amplituhedron



HomeAbstract

    Does Riemann Zeta Code for Generic Coupling Constant Evolution?

  1. Introduction

  2. Fermionic zeta as partition function and quantum criticality

    1. Could the spectrum of K\"ahler couplings strength correspond to poles of ζF(s/2)?

    2. The identification of 1/αsub>K as inverse temperature identified as pole of ζF

  3. About coupling constant evolution

    1. General description of coupling strengths in terms of complex square root of thermodynamics

    2. Does ζF with GL(2,Q) transformed argument dictate the evolution of other couplings?

    3. Questions about coupling constant evolution

  4. A model for electroweak coupling constant evolution

    1. Evolution of Weinberg angle

    2. Test for the model of electroweak coupling constant evolution



Home Abstract

    Is Non-Associative Physics and Language Possible Only in Many-Sheeted Space-Time?

  1. Introduction

  2. Is non-associative physics possible in many-sheeted space-time?

    1. What does non-associativity mean?

    2. Language and many-sheeted physics?

    3. What about the hierarchy of Planck constants?

  3. Braiding hierarchy mathematically

    1. How to represent the hierarchy of braids?

    2. Braid groups as coverings of permutation groups

    3. Braid having braids as strands

  4. General formulation for the breaking of associativity in the case of operads

    1. How associativity could be broken?

    2. An attempt to interpret



HomeAbstract

    Could N=2 Super-Conformal Algebra Be Relevant For TGD?

  1. Introduction

    1. Questions about SCS in TGD framework

    2. Questions about N=2 SCS

  2. Some CFT backround

    1. Modular invariant partition functions

    2. Degenerate conformal representations and minimal models

    3. Minimal N=2 CFTs

  3. Could N=2 SCA be relevant for TGD?

    1. How does the ADE picture about SCFTs and criticality emerge in TGD?

    2. Degrees of freedom and dynamics

    3. Covariantly constant right-handed neutrinos as generators of super-conformal symmetries

    4. Is N=2 SCS possible?

    5. How to circumvent the signature objection against N=2 SCFT?

    6. The necessity of Kac-Moody algebra of SU(2)× U(1)

    7. h=K/2 condition for Ramond representations

    8. h=K/2 condition for N-S type representations



PART IV: CATEGORIES AND TGD



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. Categorification and finite measurement resolution

      2. Inclusions of HFFs and planar tangles

      3. 2-plectic structures and TGD

      4. TGD variant for the category nCob

      5. Number theoretical universality and category theory

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

      7. Category theory and hierarchy of Planck constants



Home Abstract

    Could categories, tensor networks, and Yangians provide the tools for handling the complexity of TGD?

  1. Introduction

  2. Basic vision

    1. Very concise summary about basic notions and ideas of TGD

    2. Tensor networks as categories

    3. Yangian as a generalization of symmetries to multilocal symmetries

  3. Some mathematical background about Yangians

    1. Yang-Baxter equation (YBE)

    2. Yangian

    3. Super-Yangian

  4. Yangianization in TGD framework

    1. Geometrization of super algebras in TGD framework

    2. Questions

    3. Yangianization of four-momentum

    4. An attempt to understand binding energy at the level of Yangian

  5. Category theory as a basic tool of TGD

    1. Fusion categories

    2. Braided categories

    3. Categories with reconnections

  6. Trying to imagine the great vision

    1. Different kind of categories

    2. Geometric categories



HomeAbstract

    Are higher structures needed in the categorification of TGD?

  1. Introduction

    1. Higher structures and categorification of physics

    2. Evolution of Schreiber's ideas

    3. What higher structures are?

    4. Possible applications of higher structures to TGD

  2. TGD very briefly

    1. World of classical worlds (WCW)

    2. Strong form of holography (SH)

  3. The notion of finite measurement resolution

    1. Inclusions of HFFs, finite measurement resolution and quantum dimensions

    2. Three options for the identification of quantum dimension

    3. n-structures and adelic physics

    4. Could normal sub-groups of symplectic group and of Galois groups correspond to each other?

    5. A possible connection with number theoretic Langlands correspondence

    6. A formulation of adelic TGD in terms of cognitive representations?

  4. The notion of finite measurement resolution

    1. Inclusions of HFFs, finite measurement resolution and quantum dimensions

    2. Three options for the identification of quantum dimension

    3. n-structures and adelic physics

    4. Could normal sub-groups of symplectic group and of Galois groups correspond to each other?

    5. A formulation of adelic TGD in terms of cognitive representations?

  5. Appendix

    1. What could be the counterpart of the fake flatness in TGD framework?

    2. A little glossary



PART V: MISCELLANEOUS



HomeAbstract

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

  1. Introduction

    1. Is the analog of space-time SUSY possible in TGD?

    2. What happens when many-sheeted space-time is approximated with Minkowski space?

    3. What SUSY QFT limit could mean?

    4. Scattering amplitudes as sequences of algebraic operations

  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. Kähler-Dirac equation

    2. Development of ideas about space-time SUSY

    3. Summary about TGD counterpart of space-time SUSY

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

  4. Understanding of the role of right-handed neutrino in supersymmetry

    1. Basic vision

    2. What is the role of the right-handed neutrino?

    3. The impact from LHC and evolution of TGD itself

    4. Supersymmetry in crisis

    5. Right-handed neutrino as inert neutrino?

    6. Experimental evidence for sterile neutrino?

    7. Delicacies of the induced spinor structure and SUSY mystery

    8. Conclusions

  5. 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?



HomeAbstract

    Coupling Constant Evolution in Quantum TGD

  1. Introduction

    1. New ingredients helping to understand coupling constant evolution

    2. A sketch for the coupling constant evolution

  2. Summary of basic ideas of Quantum TGD

    1. General ideas of quantum TGD

    2. The construction of M-matrix

    3. Are both symplectic and conformal field theories needed in TGD framework?

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

    1. A general view about coupling constant evolution

    2. Coupling constant evolution as increase in computational precision in Yangian arithmetics?

    3. Could correlation functions, S-matrix, and coupling constant evolution be coded the statistical properties of preferred extremals?

  4. p-Adic coupling constant evolution

    1. General considerations

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

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

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

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

  5. Quantitative guesses 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?

    3. Super-symplectic gluons and non-perturbative aspects of hadron physics

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

    5. The formula for the hadronic string tension

  6. Appendix: Identification of the electro-weak couplings




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    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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