Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields

The following sections are included:

• Preface

• Contents

• Introduction

The following sections are included:

• Stochastic quantization

• Dynamical generation of the noise

• The free Klein-Gordon field with chaotic noise

• * Chaotic quantization in momentum space

• * Gauge fields with chaotic noise

• Distinguished properties of Tchebyscheff maps

• * Graph theoretical method

• * Perturbative approach

The following sections are included:

• Motivation for chaotic strings

• Anti-integrable limit of a continuum φ^N+1-theory

• Possible generalizations

• Yet another way to derive the chaotic string

• Symmetry properties

• Stability properties

• Fixed points

• * Spatio-temporal patterns

The following sections are included:

• Self energy of the N = 3 string

• Self energy of the N = 2 string

• Self energy for general N

• Interaction energy of chaotic strings

• * Double strings

• * Rotating strings

The following sections are included:

• Some general remarks on phase transitions

• Vacuum expectation on 1-dimensional lattices

• * Real scalar field on d-dimensional lattices

• * Complex scalar field with U(1) symmetry

• * Chaotic Higgs field with SU(2) symmetry

The following sections are included:

• Fluctuations of momenta and positions

• Newton's law and self interaction

• Coulomb forces and Laplacian coupling

• Duality of interpretations

• Feynman webs

• Physical interpretation of discrete string symmetries

• Fluctuations of the metric and a 1+1 dimensional model of quantum gravity

The following sections are included:

• Heat bath of the vacuum

• * States of maximum information

• * States of minimum correlation

• Nonextensive statistical mechanics

• Energy dependence of the entropic index q

• Fluctuations of temperature

• Klein-Gordon field with fluctuating momenta

The following sections are included:

• Analogue of the Einstein field equations

• The 3A string—electric interaction strengths of electrons and d-quarks

• The 3B string—weak interaction strengths of neutrinos and u-quarks

• High-precision prediction of the electroweak parameters

• The 2A string —strong interaction strength at the W-mass scale

• The 2B string —the lightest scalar glueball

• The 2A⁻ and 2B⁻ strings — towards a Higgs mass prediction

• Gravitational interaction

The following sections are included:

• Self interacting scalar field equations

• The 3A string —weak and strong interactions of heavy fermion flavors

• The 3B string — further mixed states of heavy fermion flavors

• The 2A string — further bosons

• The 2B string — Yukawa interaction of the top quark

• Yukawa and gravitational interactions of all quarks and leptons

• Neutrino mass prediction

• The 2A⁻ and 2B⁻ strings — bosonic mass ratios

The following sections are included:

• Hadronization of free quarks

• Mesonic states

• Baryonic states

• * CP violation

• Planck scale interpretation

• Dark matter

The following sections are included:

• Supersymmetric versus non-supersymmetric theories

• A supersymmetric scenario

• A non-supersymmetric scenario

• Final unification at the Planck scale

• Simplification for sin² θ_w = ½

• Bosons at the Planck scale

• * Some thoughts on supersymmetry

The following sections are included:

• Chaotic dynamics in compactified dimensions

• Quantized Einstein field equations

• N = 1 strings and Minkowski space

• Potentials for the N = 1 strings and inflation

• Black holes, Hawking radiation, and duality

• The limit E → ∞

• Brief history of the universe — as seen from chaotic strings

The following sections are included:

• Motivation and main results

• The chaotic string dynamics

• Vacuum energy of chaotic strings

• Fixing standard model parameters

• Numerical findings

• Physical embedding

• Conclusion

The following sections are included:

• Bibliography

• Index