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.



PART I: The notion of many-sheeted space-time||Basic Extremals of the Kähler action||About Identification of the Preferred extremals of Kähler Action||About Hydrodynamical and Thermodynamical Interpretations of TGD||General View About Physics in Many-Sheeted Space-Time||Can one apply Occam's razor as a general purpose debunking argument to TGD?||

PART II: Many-Sheeted Cosmology, and Astrophysics||TGD and GRT||TGD and Potential Anomalies of GRT ||Cosmic Strings||TGD and Cosmology||More about TGD and Cosmology||TGD and Astrophysics || Quantum Astrophysics ||What are the counterparts of Einstein's equations in TGD? ||

PART III: Topological Field Quantization and Generation of Structures
||Hydrodynamics and CP2 geometry||Macroscopic Quantum Phenomena and CP2 Geometry||Appendix||


  1. Basic Ideas of Topological Geometrodynamics (TGD)

    1. Basic vision very briefly

    2. Two manners to see TGD and their fusion

    3. Basic objections

    4. p-Adic variants of space-time surfaces

    5. The threads in the development of quantum TGD

    6. Hierarchy of Planck constants and dark matter hierarchy

    7. Twistors and TGD

  2. Bird's eye of view about the topics of the book

    1. The implications deriving from the topology of space-time surface and from the properties of induced gauge fields

    2. Many-sheeted cosmology

    3. Dark matter and quantization of gravitational Planck constant

    4. The topics of the book

  3. The contents of the book

  4. Sources

    1. PART I: The notion of many-sheeted space-time

    2. PART II: Many-Sheeted Cosmology, and Astrophysics

    3. PART III: Topological field quantization



    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. Does GRT really allow gravitons

    4. Generalization of the solution ansatz defining massless extremals

    5. Maxwell phase

    6. Stationary, spherically symmetric extremals

    7. Maxwell hydrodynamics as a toy model for TGD


    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


    General About Hydrodynamical and Thermodynamical Interpretations of TGD

  1. Hydrodynamic interpretation of extremals

    1. Possible role of Beltrami flows and symplectic invariance in the description of gauge and gravitational interactions

    2. A general solution ansatz based on almost topological QFT property

    3. Preferred extremals as perfect fluids

    4. Preferred extremals as perfect fluids

    5. Hydrodynamic picture in fermionic sector

  2. Does thermodynamics have a representation at the level of space-time geometry?

    1. Motivations and background

    2. Kiehn's topological thermodynamics (TTD)

    3. Attempt to identify TTD in TGD framework

  3. Robert Kiehn's ideas about Falaco solitons and generation of turbulent wake from TGD perspective

    1. Falaco solitons and TGD

    2. Stringy description of condensed matter physics and chemistry?

    3. New manner to understand the generation of turbulent wake


    General View About Physics in Many-Sheeted Space-Time

  1. Introduction

    1. Parton level formulation of quantum TGD

    2. Zero energy ontology

    3. Fusion of real and p-adic physics to single one

    4. Dark matter hierarchy and hierarchy of Planck constants

    5. p-Adic coupling constant evolution

  2. The new developments in quantum TGD

    1. Reduction of quantum TGD to parton level

    2. Quantum measurement theory with finite measurement resolution

    3. Hierarchy of Planck constants

    4. Zero energy ontology

    5. U- and S-matrices

    6. Number theoretic ideas

  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. Super-symplectic degrees of freedom

    1. What could happen in the transition to non-perturbative QCD?

    2. Super-symplectic bosons as a particular kind of dark matter

  5. 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 hadron physics

    6. The notion of number theoretical braid

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

  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. 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


    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?



    The relationship between TGD and GRT

  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. The problem of cosmological constant

    5. Topics of the chapter

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

    1. General Coordinate Invariance

    2. The basic objection against TGD

    3. How GRT and Equivalence Principle emerge from TGD?

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

  3. Imbedding of the Reissner-Nordström metric

    1. Two basic types of imbeddings

    2. The condition guaranteing the vanishing of em, Z0, or Kähler fields

    3. Imbedding of Reissner-Nordström metric

  4. A model for the final state of the star

    1. Spherically symmetric model

    2. Dynamo model

    3. Z0 force and dynamics of compact objects

    4. Correlation between gamma ray bursts and supernovae and dynamo model for the final state of the star

    5. Z0 force and Super Nova explosion

    6. Microscopic description of black-holes in TGD Universe

  5. TGD based model for cosmic strings

    1. Zero energy ontology and cosmic strings

    2. Topological condensation of cosmic strings

    3. Dark energy is replaced with dark matter in TGD framework

    4. The values for the TGD counterpart of cosmological constant

    5. Matter-antimatter asymmetry and cosmic strings

  6. Entropic gravity in TGD framework

    1. The phenomenology of EG in TGD framework

    2. The conceptual framework of TGD

    3. What can one conclude?

  7. Emergent gravity and dark Universe

    1. Verlinden's argument

    2. The long range correlations of Verlinde correspond to hierarchy of Planck constants in TGD framework

    3. The argument against gravitation as entropic force can be circumvented in zero energy ontology


    TGD and Potential Anomalies of GRT

  1. Introduction

  2. Allais effect and TGD

    1. The effect

    2. Could gravitational screening explain Allais effect

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

    4. Could Z0 force be present?

  3. Gravimagnetism and TGD

    1. Gravity Probe B and TGD

    2. Does horizon correspond to a degenerate four-metric for the rotating counterpart of Schwartshild metric?

    3. Has strong gravimagnetism been observed?

    4. Is the large gravimagnetic field possible in TGD framework?

  4. Some differences between GRT and TGD

    1. Do neutrinos travel with superluminal speed?

    2. Anomalous time dilation effects due to warping as basic distinction between TGD and GRT

    3. Evidence for many-sheeted space-time from gamma ray flares

    4. Is gravitational constant really constant?

  5. Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity?

    1. The predictions of TGD for the local light-velocity

    2. The analysis of Cahill of the measurements trying to measure absolute motion

    3. Cahill's work in relation to TGD

  6. Miscellaneous topics

    1. Mickelson-Morley experiment revisited

    2. Einstein's equations and second variation of volume element

    3. Various interpretations of Machian Principle in TGD framework


    Cosmic strings

  1. Introduction

    1. Various strings

    2. Equivalence Principle and cosmic strings

    3. TGD based quantum model for astrophysical systems

    4. Correlation between super-novae and cosmic strings

  2. General vision about topological condensation of cosmic strings

    1. Free cosmic strings

    2. TGD based model for topologically condensed cosmic strings

  3. More detailed view about topological condensation of cosmic strings

    1. Topological condensation of a positive energy cosmic string

    2. Exterior metrics of cosmic string as extremal of curvature scalar

    3. Exterior metric of negative energy cosmic string with large angle excess

    4. Geodesic motion in the exterior metric of the negative energy cosmic string

    5. Matter distribution around cosmic string

    6. Quantization of the cosmic recession velocity

  4. Cosmic evolution and cosmic strings

    1. Cosmic strings and generation of structures

    2. Generation of ordinary matter via TGD counterpart of Hawking radiation?

    3. How single cosmic string could reduce its Kähler string tension?

    4. Zero energy ontology, cosmic strings, and consciousness

    5. A new cosmological finding challenging General Relativity

  5. Cosmic string model for galaxies and other astrophysical objects

    1. Cosmic strings and the organization of galaxies into linear structures

    2. Cosmic strings and dark matter problem

    3. Estimate for the velocity parameters

    4. Galaxies as split cosmic strings?

    5. Cylindrically symmetric model for the galactic dark matter

    6. New information about the distribution of galactic dark matter

    7. Cold dark matter in difficulties

    8. Three blows against standard view about dark matter

    9. Do galaxies have preferred handedness?

  6. Cosmic strings and energy production in quasars

    1. Basic properties of the decaying cosmic strings

    2. Decaying cosmic string ends as a central engine

    3. How to understand the micro-jet structure?

    4. Gamma-ray bursts and cosmic strings

  7. The light particles associated with dark matter and the correlation between gamma ray bursts and supernovae

    1. Correlations between gamma ray bursts and supernovae

    2. Lepto-pions as a signature dark matter?


    TGD and Cosmology

  1. Introduction

    1. Zero energy cosmology

    2. Dark matter hierarchy and hierarchy of Planck constants

    3. Quantum criticality and quantum phase transitions

    4. Critical and over-critical cosmologies are highly unique

    5. Equivalence Principle in TGD framework

    6. Cosmic strings as basic building blocks of TGD inspired cosmology

    7. Topics of the chapter

  2. Basic ingredients of TGD inspired cosmology

    1. Many-sheeted space-time defines a hierarchy of smoothed out space-times

    2. Robertson-Walker cosmologies

    3. Cosmic strings and cosmology

    4. Thermodynamical considerations

    5. Structure of WCW in zero energy ontology and Robertson-Walker cosmology

  3. TGD inspired cosmology

    1. Primordial cosmology

    2. Critical phases

    3. Radiation dominated phases

    4. Matter dominated phases

    5. Stationary cosmology

  4. Inflationary cosmology or quantum critical cosmology?

    1. Comparison with inflationary cosmology

    2. Balloon measurements of the cosmic microwave background favor flat cosmos

    3. Quantum critical fractal cosmology as TGD counterpart of the inflationary cosmology

    4. The problem of cosmological missing mass

    5. TGD based explanation of the results of the balloon experiments

  5. Inflation and TGD

    1. Brief summary of the inflationary scenario

    2. The problems that inflation was proposed to solve

    3. Comparison with TGD inspired cosmology

  6. BICEP2 might have detected gravitational radiation

    1. Comparison of inflationary model and TGD

    2. Inflation should beging at GUT mass scale

    3. Fluctuations of gravitational field

    4. Inflation should begin at GUT scale

    5. Difficulties of the inflationary approach

    6. Could TGD allow inflationary cosmology

    7. Quantum critical cosmology of TGD predicts also very fast expansion

    8. Still comments abount inflation in TGD

    9. Could the polarization be due to synchrotron radiation?

  7. Cyclic cosmology from TGD perspective

    1. Extreme complexity of theories vizĀ·

    2. Why the cosmology is so homogenous and isotropic?

    3. The TGD analog of cyclic cosmology


    More about TGD and Cosmology

  1. Introduction

    1. Zero energy cosmology

    2. Dark matter hierarchy and hierarchy of Planck constants

    3. Quantum criticality and quantum phase transitions

    4. Critical and over-critical cosmologies are highly unique

    5. Equivalence Principle in TGD framework

    6. Cosmic strings as basic building blocks of TGD inspired cosmology

    7. Topics of the chapter

  2. About the anomalies of the cosmic microwave background

    1. Background

    2. Anomalies CMB

    3. What TGD could say about the anomalies?

  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. Conclusions

    6. Five years later

  4. Some problems of cosmology

    1. Antimatter as dark matter?

    2. Why some stars seem to be older than the Universe? /font>

    3. Mechanism of accelerated expansion in TGD Universe

    4. New anomaly in Cosmic Microwave Background

    5. Could many-sheeted cosmology explain the claimed time dependence of the fine structure constant?

    6. Apparent time dependence of the fine structure constant

    7. The redshift anomaly of quasars

    8. The problem of fermion families

  5. Matter-antimatter asymmetry, baryo-genesis, lepto-genesis, and TGD

    1. Background

    2. Could TGD allow matter-antimatter asymmetry and baryo-genesis?

  6. Quantum fluctuations in geometry as a new kind of noise?

    1. The experiment

    2. Hogan's theory

    3. TGD based model

  7. Could hyperbolic 3-manifolds and hyperbolic lattices be relevant in zero energy ontology?

    1. Hyperbolic lattices in H3 from zero energy ontology

    2. Comparing crystallographies in E3 and H3

    3. About congruence groups

    4. Quasicrystals

    5. Could quasi-lattices and quasi-crystals emerge from the notion of p-adic manifold?

  8. Does the rate of cosmic expansion oscillate?

    1. TGD based model for the findings

    2. Appendix: p-adic length scale hypothesis and Gaussian Mersennes

  9. Correlated Triangles and Polygons in Standard Cosmology and in TGD

    1. Could cosmic microwave background exhibit non-local correlations?

    2. Early cosmology in TGD framework

    3. How do polygons emerge in TGD framework?

    4. Symplectic invariants and Abelian non-integrable phase factors


    TGD and Astrophysics

  1. Introduction

    1. p-Adic length scale hypothesis and astrophysics

    2. Quantum criticality, hierarchy of dark matters, and dynamical hbar

    3. Dark matter as a source of long range color and electro-weak fields

  2. p-Adic length scale hypothesis at astrophysical and cosmological length scales

    1. List of long p-adic length scales

    2. p-Adic evolution of cosmological constant

    3. Evidence for a new length scale in cosmology

  3. Solar magnetic fields and Sunspot cycle

    1. Sunspot cycle

    2. Sunspots as helical vortices

    3. A model for the Sunspot cycle

    4. Helical vortex as a model for a magnetic flux tube

    5. Estimates for the vacuum parameters of magnetic flux tube

  4. Explanation for the high temperature of solar corona

    1. Topological model for the magnetic field of Sun

    2. Quantitative formulation

  5. Explanations of some astrophysical and cosmological anomalies

    1. Apparent shrinking of solar system

    2. Pioneer anomaly

    3. In what sense speed of light could be changing in solar system?

    4. Flyby anomaly

    5. Pioneer and Flyby anomalies for almost decade later

    6. Further progress in the understanding of dark matter and energy in TGD framework

  6. Do we really understand the solar system?

    1. Motivations

    2. A model for the motion of comet in the gravitational field of flux tube

    3. A model for the precession of the solar system in the gravitational field of flux tube

    4. Cosmic evolution as transformation of dark energy to matter

    5. The origin of cosmic rays

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

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

    2. The interpretation of the parameter v0

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

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

    9. About the interpretation of the parameter v0

    10. The challenge of six planets

  8. Further indications for dark matter

    1. Some anomalies

    2. Anti-matter and dark matter

  9. Explanations of some astrophysical and cosmological anomalies

    1. Apparent shrinking of solar system

    2. In what sense speed of light could be changing in solar system?

    3. Pioneer anomaly

    4. Fly-by anomaly

    5. Pioneer and Flyby anomalies for almost decade later

    6. Further progress in the understanding of dark matter and energy in TGD framework

    7. Variation of Newston's constant and of length of day

    8. The new findings about the structure of Milky from TGD viewpoint

    9. Is Dragonfly a "failed" galaxy?

    10. TGD interpretation for the new discovery about galactic dark matter

    11. Bullet cluster, cold dark matter, and MOND

  10. Appendix: Orbital radii of exo-planets as a test for the theory


    Quantum Astrophysics

  1. Introduction

    1. Generalization of the notion of imbedding space

    2. Gravitational Bohr orbitology

    3. How General Coordinate Invariance and Lorentz invariance are achieved?

  2. Updated view about the hierarchy of Planck constants

    1. Basic physical ideas

    2. Space-time correlates for the hierarchy of Planck constants

    3. Basic phenomenological rules of thumb in the new framework

    4. Charge fractionalization and anyons

    5. What about the relationship of gravitational Planck constant to ordinary Planck constant?

    6. Summary

  3. General quantum vision about formation of structures

    1. Simple quantitative model

    2. Formation of rings like structures

    3. A quantum model for the dark part of the central mass and rings

    4. Two stellar components in the halo of Milky Way

  4. Quantum chaos in astrophysical length scales

    1. Brief summary about quantum chaos

    2. What does the transition to quantum chaos mean?

    3. Quantum chaos in astrophysical scales?

  5. Gravitational radiation and large value of gravitational Planck constant

    1. Standard view about gravitational radiation

    2. Quantum mechanisms for the emission of gravitational radiation

    3. Model for dark gravitons

    4. Detection of gravitational radiation

    5. Quantitative model

    6. Generalization to gauge interactions

    7. Can graviton have mass?

  6. LIGO and TGD

    1. Some history

    2. What was observed?

    3. Are observations consistent with TGD predictions?

    4. Appendix: Some details about rotating and charged blackholes

  7. Piece-wise accelerated cosmic expansion as basic prediction of quantum cosmology

    1. Experimental evidence for accelerated expansion is consistent with TGD based model

    2. Quantum version of Expanding Earth theory

  8. Implications Expanding Earth model for the pre-Cambrian evolution of continents, of climate, and of life

    1. Super-continent theory

    2. Standard view about oceans

    3. Glaciations during Neoproterozoic period

    4. Snowball Earth model for the glaciation during pre-Cambrian era

    5. TGD point of view about pre-Cambrian period

    6. Paleo-magnetic data and Expanding Earth model

    7. Did life go underground during pre-Cambrian glaciations?

  9. Do blackholes and blackhole evaporation have TGD counterparts?

    1. Background

    2. About basic assumptions about blackhole evaporation as seen in TGD context

    3. Relating the terminology of blackhole evaporation to TGD framework

    4. Could blackhole evaporation have a TGD counterpart?

  10. New view about blackholes

    1. Anyonic view about black holes

    2. Super-symplectic bosons

    3. Are ordinary blackholes replaced with super-symplectic blackholes?

    4. Blackholes do not absorb dark matter so fast as they should


    What are the counterparts of Einstein's equations in TGD?

  1. Introduction

  2. Light-like 3-surfaces as vacuum solutions of 3-D vacuum Einstein equations and Witten's approach to quantum gravitation

    1. Similarities with TGD

    2. Differences from TGD

  3. Entropic gravity and TGD

    1. Verlinde's argument for F=ma

    2. Verlinde's argument for F= GMm/R2

    3. In TGD quantum classical correspondence predicts that thermodynamics has space-time correlates

    4. The simplest identification of thermodynamical correlates in TGD framework

    5. Some details related to the measurement interaction term

  4. What could be the counterparts of Einstein's equations in TGD

    1. Could a deformation of the metric of E3 preserving SO(3) symmetry allow to make the the tetrahedra in the decomposition of icosahedron regular?

    2. Appendix A: Does TGD force a modification of Einstein equations?

    3. Appendix B: Conditions on function k(r) from the generalization of Einstein's equations for vacuum extremals

    4. Appendix C: The regular tetrahedron property is not possible for k=constant option



    Hydrodynamics and CP2 geometry

  1. Introduction

    1. Basic ideas and concepts

    2. Z0 magnetic fields and hydrodynamics

    3. Topics of the chapter

  2. Many-sheeted space-time concept

    1. Basic concepts related to topological condensation and evaporation

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

    3. Number theoretical considerations

    4. Physically interesting p-adic length scales in condensed matter systems

  3. Hydrodynamical and thermodynamical hierarchies

    1. Dissipation by the collisions of condensate blocks

    2. Energy transfer between different condensate levels in turbulent flow

    3. The magnetic fields associated with vortex and rigid body flows

    4. Criticality condition

    5. Sono-luminescence and hydrodynamical hierarchy

    6. p-Adic length scale hypothesis, hydrodynamic turbulence, and distribution of primes

    7. Thermodynamic Hierarchy

  4. Configuration space geometry and phase transitions

    1. Basic ideas of catastrophe theory

    2. Configuration space geometry and catastrophe theory

    3. Quantum TGD and catastrophe theory

    4. TGD based description of phase transitions

  5. Imbeddings of the cylindrically symmetric flows

    1. The general form of the imbedding of the cylindrically symmetric rotational flow.

    2. Orders of magnitude for some vacuum parameters

    3. Critical radii for some special flows

  6. Transition to turbulence in channel flow

    1. Transition to turbulence

    2. Definition of the model

    3. Estimates for the parameters

    4. Kähler fields associated with the cascade process

    5. Order of magnitude estimate for the change of the Kähler action and Reynolds criterion

    6. Phase slippage as mechanism for the decay of vortices


    Macroscopic quantum phenomena and CP2 geometry

  1. General Theory

    1. Identification of the topological field quanta

    2. Formation of the supra phase

    3. Generalized quantization conditions

    4. Dissipation in super fluids: critical velocities

    5. Meissner effect

    6. Phase slippage

  2. Models for topological field quanta

    1. The Kähler field created by a constant mass distribution

    2. The imbedding of a constant magnetic fields

    3. Magnetic fields associated with constant velocity flows

  3. Quantum Hall effect from topological field quantization

    1. The effect

    2. The model

  4. TGD and condensed matter

    1. Electronic conductivity and topological field quantization

    2. Dielectrics and topological field quantization

    3. Magnetism and topological field quantization



  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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