I am grateful for comments, criticism and suggestions. The following list gives table of contents for "TGD: Physics as Infinite-Dimensional Geometry". If You want, say chapter "Configuration Space Spinor Structure", as a .pdf file, just click on "Configuration Space Spinor Structure" 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.


PART I: p-Adic description of particle massivation
|| Overall view about TGD from particle physics perspective || WCW Spinor Structure||Elementary Particle Vacuum Functionals||Massless states and particle massivation|| p-Adic particle massivation: hadron masses ||
||PART II: New Physics predicted by TGD
||Higgs or Something Else? ||SUSY in TGD Universe ||New Particle Physics Predicted by TGD: I||New Particle Physics Predicted by TGD: II||


  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. Bird's eye of view about the contents of the book

  4. The contents of the book

    1. PART I: p-Adic description of particle massivation

    2. PART II: TGD and p-adic length scale hypothesis



    Overall View about TGD from Particle Physics Perspective

  1. Introduction

  2. Some aspects of quantum TGD

    1. New space-time concept

    2. Zero energy ontology

    3. The hierarchy of Planck constants

    4. p-Adic physics and number theoretic universality

  3. Symmetries of quantum TGD

    1. General Coordinate Invariance

    2. Generalized conformal symmetries

    3. Equivalence Principle and super-conformal symmetries

    4. Extension of super-conformal symmetries

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

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

  4. 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?

  5. Quantum TGD very briefly

    1. Two approaches to quantum TGD

    2. Overall view Kähler action and Kähler Dirac action

    3. Various Dirac operators and their interpretation

    4. Is the effective metric effectively one- or two-dimensional?

  6. Summary of generalized Feynman diagrammatics

    1. The basic action principle

    2. A proposal for M-matrix


    WCW Space 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


    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. Identification of elementary particles

    1. Elementary fermions and bosons

    2. Graviton and other stringy states

    3. Spectrum of non-stringy states

  3. Basic facts about Riemann surfaces

    1. Mapping class group

    2. Teichmueller parameters

    3. Hyper-ellipticity

    4. Theta functions

  4. 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

  5. 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?

    4. Could higher genera have interpretation as many-particle states?

  6. Elementary particle vacuum functionals for dark matter

    1. Hurwitz zetas cannot correspond to dark matter in TGD sense

    2. ζH(s,1/2)$ inspires an explanation for why the number of fermion generations is three

    3. About Hurwitz zetas


    Massless States and Particle Massivation

  1. Introduction

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

    2. Particle massivation

    3. What next?

  2. Identification of elementary particles

    1. Partons as wormhole throats and particles as bound states of wormhole contacts

    2. Family replication phenomenon topologically

    3. Critizing the view about elementary particles

  3. Non-topological contributions to particle masses from p-adic thermodynamics

    1. Partition functions are not changed

    2. Fundamental length and mass scales

    3. Color degrees of freedom

    4. Spectrum of elementary particles

    5. Some probabilistic considerations

  4. Modular contribution to the mass squared

    1. Conformal symmetries and modular invariance

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

    3. Generalization of Θ functions and quantization of p-adic moduli

    4. The calculation of the modular contribution to the conformal weight

  5. The contributions of p-adic thermodynamics to particle masses

    1. General mass squared formula

    2. Color contribution to the mass squared

    3. Modular contribution to the mass of elementary particle

    4. Thermal contribution to the mass squared

    5. The contribution from the deviation of ground state conformal weight from negative integer

    6. General mass formula for Ramond representations

    7. General mass formulas for NS representations

    8. Primary condensation levels from p-adic length scale hypothesis

  6. Fermion masses

    1. Charged lepton mass ratios

    2. Neutrino masses

    3. Quark masses

  7. About the microscopic description of gauge boson massivation

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

    2. The counterpart of Higgs vacuum expectation in TGD

    3. Elementary particles in ZEO

    4. Virtual and real particles and gauge conditions in ZEO

    5. The role of string world sheets and magnetic flux tubes in massivation

    6. Weak Regge trajectories

  8. About the basic assumptions behind p-adic mass calculations

    1. Why p-adic thermodynamics?

    2. How to understand the conformal weight of the ground state?

    3. What about Poincare invariance?

    4. What are the fundamental dynamical objects?

    5. What about the identification of conformal symmetries?

  9. Appendix: The particle spectrum predicted by TGD

    1. The general TGD based view about elementary particles

    2. Construction of single fermion states

    3. About the construction of mesons and elementary bosons in TGD Universe

    4. What SUSY could mean in TGD framework?


    p-Adic Particle Massivation: Hadron Masses

  1. Introduction

    1. Construction of U and D matrices

    2. Observations crucial for the model of hadron masses

    3. A possible model for hadron

  2. Quark masses

    1. Basic mass formulas

    2. The p-adic length scales associated with quarks and quark masses

    3. Are scaled up variants of quarks also there?

  3. Topological mixing of quarks

    1. Mixing of the boundary topologies

    2. The constraints on U and D matrices from quark masses

    3. Constraints from CKM matrix

  4. Construction of U, D and CKM matrices

    1. The constraints from CKM matrix and number theoretical conditions

    2. How strong mumber theoretic conditions one can pose on U and D matrices

    3. Could rational unitarity make sense?

    4. The parametrization suggested by the mass squared conditions

    5. Thermodynamical model for the topological mixing

    6. U and D matrices from the knowledge of top quark mass alone?

  5. Hadron masses

    1. The definition of the model for hadron masses

    2. The anatomy of hadronic space-time sheet

    3. Pseudoscalar meson masses

    4. Baryonic mass differences as a source of information

    5. Color magnetic spin-spin splitting

    6. Color magnetic spin-spin interaction and super-canonical contribution to the mass of hadron

    7. Summary about the predictions for hadron masses

    8. Some critical comments



    Higgs Or Something Else?

  1. Introduction

    1. Can one do without standard model Higgs?

    2. Why Higgs like particle is needed?

    3. The recent situation

  2. Background

    1. GUT paradigm

    2. How to achieve separate conservation of $B$ and $L$?

    3. Particle massivation from p-adic thermodynamics

    4. The conservation of em charge in TGD framework

  3. About the microscopic description of gauge boson massivation

    1. The counterpart of Higgs vacuum expectation in TGD

    2. Elementary particles in ZEO

    3. Virtual and real particles and gauge conditions in ZEO

    4. The role of string world sheets and magnetic flux tubes in massivation

    5. Weak Regge trajectories

    6. Low mass exotic mesonic structures as evidence for dark scaled down variants of weak bosons?

    7. Cautious conclusions

  4. Two options for Higgs like states in TGD framework

    1. Two options concerning the interpretation of Higgs like particle in TGD framework

    2. Space-time correlate for stringy mass shell condition and analog of Higgs expectation

    3. Microscopic description of gauge bosons and Higgs like and meson like states

    4. Trying to understand the QFT limit of TGD

    5. To deeper waters

    6. Criticality of Higgs: is Planck length dogmatics physically feasible?

  5. 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


    SUSY in TGD Universe

  1. Introduction

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

    1. K\"ahler-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

  3. 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

  4. Experimental situation

    1. Almost predictions related to SUSY

    2. Goodbye large extra dimensions and MSSM

    3. Do X and Y mesons provide evidence for color excited quarks or squarks?

    4. Strange trilepton events at CMS

    5. CMS observes large diphoton excess

    6. No SUSY dark matter and too small electron dipole moment for standard SUSY

    7. Leptoquarks as first piece of evidence for TGD based view about SUSY?}


    New Particle Physics Predicted by TGD: Part I

  1. Introduction

  2. Family replication phenomenon

    1. Family replication phenomenon for bosons

    2. Higher gauge boson families

    3. The physics of M-M* systems forces the identificaiton of vertices as branchings of partonic 2-surfaces

  3. Dark matter in TGD Universe

    1. Dark matter and energy in TGD Universe

    2. Shy positrons

    3. Dark matter puzzle

    4. AMS results about dark matter

  4. Scaled variants of quarks and leptons

    1. Fractally scaled up versions of quarks

    2. Toponium at 30.4 GeV

    3. Could neutrinos appear in several p-adic mass scales?

  5. Scaled variants of hadron physics and weak bosons

    1. Leptohadron physics

    2. First evidence for M89 hadron physics

    3. Other indications for M89 hadron physics

    4. LHC might have produced new matter: are M89 hadrons in question?

    5. New results from PHENIX concerning quark gluon plasma

    6. Anomalous like sign dimuons at LHC?

    7. Could MG,79 hadron physics be seen at LHC?

    8. Has IceCube detected neutrinos coming from decays of p-adically scaled up copies of weak bosons?

    9. Some comments about τ-μ anomaly of Higgs decays and anomalies of B meson decays

  6. QCD and TGD

    1. How the TGD based notion of color differs from QCD color

    2. Basic differences between QCD and TGD

    3. p-Adic physics and strong interactions

    4. Magnetic flux tubes and and strong interactions

    5. Does color confinement really occur?

    6. Exotic pion like states: "infra-red" Regge trajectories or Shnoll effect?

  7. Cosmic rays and Mersenne primes

    1. Mersenne primes and mass scales

    2. Cosmic strings and cosmic rays

    3. Centauro type events, Cygnus X-3 andM89 hadrons

    4. TGD based explanation of the exotic events

    5. Cosmic ray spectrum and exotic hadrons

    6. Ultrahigh energy cosmic rays as super-symplectic quanta?

  8. Have lepto-quarks been observed in the decays of B mesons?

    1. General ideas

    2. A TGD based model for the B anomaly in terms of lepto-quarks

  9. New indications for the new physics predicted by TGD

    1. Some almost predictions of TGD

    2. Indications for the new physics

    3. Muon surplus in high energy cosmic ray showers as an indication for new hadron physics

    4. Is the new physics really so elementary as believed?


    New Particle Physics Predicted by TGD: Part II

  1. Introduction

    1. Application of the many-sheeted space-time concept in hadron physics

    2. Quark gluon plasma

    3. Breaking of discrete symmetries

    4. Are exotic Super Virasoro representations relevant for hadron physics?

  2. New space-time concept applied to hadrons

    1. A new twist in the spin puzzle of proton

    2. Topological evaporation and the concept of Pomeron

    3. The incredibly shrinking proton

    4. Misbehaving b-quarks and the magnetic body of proton

    5. Explanation for the soft photon excess in hadron production

  3. Simulating Big Bang in laboratory

    1. Experimental arrangement and findings

    2. TGD based model for the quark-gluon plasma

    3. Further experimental findings and theoretical ideas

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

    5. Very cautious conclusions

    6. Five years later

    7. Evidence for TGD view about QCD plasma

  4. Breaking of discrete symmetries

    1. Experimental inputs

    2. Discrete symmetries in zero energy ontology

    3. An attempt to build a concrete model for the breaking of discrete symmetries

  5. TGD based explanation for the anomalously large direct CP violation in K→ 2π decay

    1. How to solve the problems in TGD framework

    2. Basic notations and concepts

    3. Separation of short and long distance physics using operator product expansion

  6. Wild speculations about non-perturbative aspects of hadron physics and exotic Super Virasoro representations

    1. Exotic Super-Virasoro representations

    2. Could hadrons correspond to exotic Super-Virasoro representations and quark-gluon plasma to the ordinary ones?

  7. Appendix

    1. Effective Feynman rules and the effect of top quark mass on the effective action

    2. U and D matrices from the knowledge of top quark mass alone?

  8. Figures and Illustrations



  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

To the index page