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.



PHYSICS IN MANY-SHEETED SPACE-TIME



||Introduction||

PART I: The notion of many-sheeted space-time||Basic Extremals of the Kähler action||General View About Physics in Many-Sheeted Space-Time: Part I||General View About Physics in Many-Sheeted Space-Time: Part II||

PART II: Many-Sheeted Cosmology, and Astrophysics||TGD and GRT||Cosmic Strings||TGD and Cosmology||TGD and Astrophysics || Quantum Astrophysics ||

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



Introduction

  1. Basic ideas of TGD

    1. TGD as a Poincare invariant theory of gravitation

    2. TGD as a generalization of the hadronic string model

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

  2. The five threads in the development of quantum TGD

    1. Quantum TGD as configuration space spinor geometry

    2. p-Adic TGD

    3. TGD as a generalization of physics to a theory 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: Many-Sheeted Cosmology and Astrophysics

    2. PART II: Topological Field Quantization



PART I: MANY-SHEETED SPACE-TIME



HomeAbstract

    Basic extremals of the Kähler action

  1. Introduction

  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



HomeAbstract

    General View About Physics in Many-Sheeted Space-Time : Part I

  1. What do space-like 3-surfaces look like?

    1. Renormalization group invariance, quantum criticality and topology of 3-space

    2. 3-surfaces can have outer boundaries

    3. Topological field quantization

  2. Basic phenomenology of topological condensation}{14}

    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. The new space time picture and some of its consequences

    1. Topological condensation and formation of bound states

      1. 3-topology and chemistry

      2. 3-topology and super-conductivity

      3. Macroscopic bodies as a topology of 3-space

    2. Topological condensation and color confinement

      1. Explanation of color confinement using quantum classical correspondence

      2. Hadrons as color magnetic/electric flux tubes

      3. Color confinement and generation of macro-temporal quantum coherence



HomeAbstract

    General View About Physics in Many-Sheeted Space-Time: Part II

  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. 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

    3. Coupling constant evolution in Quantum TGD

  6. 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?

  7. 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

  8. 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?

  9. 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



PART II: MANY-SHEETED COSMOLOGY, AND ASTROPHYSICS



HomeAbstract

    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. Equivalence Principle

    3. Long length scale limit of TGD as General Relativity with sub-manifold constraint

    4. Mickelson-Morley experiment revisited

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

    6. Various interpretations of Machian Principle 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 K\"ahler 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. 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?

  7. 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?

  8. Some differences between GRT and TGD

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

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

    3. Is gravitational constant really constant?



HomeAbstract

    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

  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?



HomeAbstract

    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 TGD?

    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. Some problems of cosmology

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

    2. Mechanism of accelerated expansion in TGD Universe

    3. New anomaly in Cosmic Microwave Background

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

    5. Apparent time dependence of the fine structure constant

    6. The problem of fermion families

  6. 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



HomeAbstract

    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. 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. Quantum interpretation of gravitational Schrödinger equation

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

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

    10. About the interpretation of the parameter v0

    11. Further evidence for dark matter

  6. 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



HomeAbstract

    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. 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

  3. 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?

  4. 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

  5. New view about blackholes

    1. Anyonic view about black holes

    2. super-symplectic bosons

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

  6. 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

  7. 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?

  8. About the anomalies of the cosmic microwave background

    1. Background

    2. Anomalies CMB

    3. What TGD could say about the anomalies?

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

    1. The experiment

    2. Hogan's theory

    3. TGD based model

  10. Appendix

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

    2. Orbital radii of exo-planets as a test for the theory



PART III: TOPOLOGICAL FIELD QUANTIZATION



HomeAbstract

    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



HomeAbstract

    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



Home

    Appendix

  1. Basic properties of CP2

    1. CP2 as a manifold

    2. Metric and Kähler structures of CP2

    3. Spinors in CP2

    4. Geodesic sub-manifolds of CP2

  2. CP2 geometry and standard model symmetries

    1. Identification of the electro-weak couplings

    2. Discrete symmetries

  3. Basic facts about induced gauge fields

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

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

  4. p-Adic numbers and TGD

    1. p-Adic number fields

    2. Canonical correspondence between p-adic and real numbers



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