| Preface | vii |
| Introduction | xiii |
Chapter 1 | Chaotic quantization of field theories | 1 |
1.1 | Stochastic quantization | 1 |
1.2 | Dynamical generation of the noise | 3 |
1.3 | The free Klein-Gordon field with chaotic noise | 6 |
1.4 | Chaotic quantization in momentum space | 9 |
1.5 | Gauge fields with chaotic noise | 11 |
1.6 | Distinguished properties of Tchebyscheff maps | 13 |
1.7 | Graph theoretical method | 17 |
1.8 | Perturbative approach | 23 |
Chapter 2 | Chaotic strings | 27 |
2.1 | Motivation for chaotic strings | 27 |
2.2 | Anti-integrable limit of a continuum [phi superscript N+1]-theory | 30 |
2.3 | Possible generalizations | 33 |
2.4 | Yet another way to derive the chaotic string | 35 |
2.5 | Symmetry properties | 38 |
2.6 | Stability properties | 41 |
2.7 | Fixed points | 44 |
2.8 | Spatio-temporal patterns | 47 |
Chapter 3 | Vacuum energy of chaotic strings | 57 |
3.1 | Self energy of the N = 3 string | 57 |
3.2 | Self energy of the N = 2 string | 60 |
3.3 | Self energy for general N | 62 |
3.4 | Interaction energy of chaotic strings | 65 |
3.5 | Double strings | 67 |
3.6 | Rotating strings | 69 |
Chapter 4 | Phase transitions and spontaneous symmetry breaking | 75 |
4.1 | Some general remarks on phase transitions | 75 |
4.2 | Vacuum expectation on 1-dimensional lattices | 79 |
4.3 | Real scalar field on d-dimensional lattices | 82 |
4.4 | Complex scalar field with U (1) symmetry | 90 |
4.5 | Chaotic Higgs field with SU (2) symmetry | 92 |
Chapter 5 | Stochastic interpretation of the uncertainty relation | 95 |
5.1 | Fluctuations of momenta and positions | 95 |
5.2 | Newton's law and self interaction | 97 |
5.3 | Coulomb forces and Laplacian coupling | 99 |
5.4 | Duality of interpretations | 103 |
5.5 | Feynman webs | 104 |
5.6 | Physical interpretation of discrete string symmetries | 106 |
5.7 | Fluctuations of the metric and a 1+1 dimensional model of quantum gravity | 108 |
Chapter 6 | Generalized statistical mechanics approach | 113 |
6.1 | Heat bath of the vacuum | 113 |
6.2 | States of maximum information | 116 |
6.3 | States of minimum correlation | 118 |
6.4 | Nonextensive statistical mechanics | 119 |
6.5 | Energy dependence of the entropic index q | 124 |
6.6 | Fluctuations of temperature | 126 |
6.7 | Klein-Gordon field with fluctuating momenta | 129 |
Chapter 7 | Interaction energy of chaotic strings | 131 |
7.1 | Analogue of the Einstein field equations | 131 |
7.2 | The 3A string--electric interaction strengths of electrons and d-quarks | 133 |
7.3 | The 3B string--weak interaction strengths of neutrinos and u-quarks | 136 |
7.4 | High-precision prediction of the electroweak parameters | 139 |
7.5 | The 2A string--strong interaction strength at the W-mass scale | 141 |
7.6 | The 2B string--the lightest scalar glueball | 144 |
7.7 | The 2A[superscript -] and 2B[superscript -] strings--towards a Higgs mass prediction | 145 |
7.8 | Gravitational interaction | 148 |
Chapter 8 | Self energy of chaotic strings | 151 |
8.1 | Self interacting scalar field equations | 151 |
8.2 | The 3A string--weak and strong interactions of heavy fermion flavors | 152 |
8.3 | The 3B string--further mixed states of heavy fermion flavors | 156 |
8.4 | The 2A string--further bosons | 158 |
8.5 | The 2B string--Yukawa interaction of the top quark | 160 |
8.6 | Yukawa and gravitational interactions of all quarks and leptons | 162 |
8.7 | Neutrino mass prediction | 168 |
8.8 | The 2A[superscript -] and 2B[superscript -] strings--bosonic mass ratios | 172 |
Chapter 9 | Total vacuum energy of chaotic strings | 175 |
9.1 | Hadronization of free quarks | 175 |
9.2 | Mesonic states | 179 |
9.3 | Baryonic states | 182 |
9.4 | CP violation | 186 |
9.5 | Planck scale interpretation | 186 |
9.6 | Dark matter | 187 |
Chapter 10 | Grand unification | 191 |
10.1 | Supersymmetric versus non-supersymmetric theories | 191 |
10.2 | A supersymmetric scenario | 194 |
10.3 | A non-supersymmetric scenario | 196 |
10.4 | Final unification at the Planck scale | 198 |
10.5 | Simplification for sin[superscript 2] [theta subscript W] = 1/2 | 200 |
10.6 | Bosons at the Planck scale | 202 |
10.7 | Some thoughts on supersymmetry | 203 |
Chapter 11 | 11-dimensional space-time and quantum gravity | 207 |
11.1 | Chaotic dynamics in compactified dimensions | 207 |
11.2 | Quantized Einstein field equations | 210 |
11.3 | N = 1 strings and Minkowski space | 213 |
11.4 | Potentials for the N = 1 strings and inflation | 215 |
11.5 | Black holes, Hawking radiation, and duality | 217 |
11.6 | The limit E [right arrow] [infinity] | 220 |
11.7 | Brief history of the universe--as seen from chaotic strings | 222 |
Chapter 12 | Summary | 229 |
12.1 | Motivation and main results | 229 |
12.2 | The chaotic string dynamics | 232 |
12.3 | Vacuum energy of chaotic strings | 234 |
12.4 | Fixing standard model parameters | 237 |
12.5 | Numerical findings | 240 |
12.6 | Physical embedding | 247 |
12.7 | Conclusion | 249 |
| Bibliography | 253 |
| Index | 267 |