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E-raamat: Spatio-temporal Chaos and Vacuum Fluctuations of Quantized Fields illustrated edition [World Scientific e-raamat]

(Univ Of London, Uk)
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Spatio-temporal Chaos and Vacuum Fluctuations of Quantized Fields illustrated editionSuurem pilt
Teised raamatud teemal:
World Scientific e-raamatudRohkem infot World Scientific e-raamatute kohta
Raamatu kodulehekülg: http://www.worldscientific.com/worldscibooks/10.1142/4853#t=toc
This book describes new applications for spatio-temporal chaotic dynamical systems in elementary particle physics and quantum field theories. The stochastic quantization approach of Parisi and Wu is extended to more general deterministic chaotic processes as generated by coupled map lattices. In particular, so-called chaotic strings are introduced as a suitable small-scale dynamics of vacuum fluctuations. This more general approach to second quantization reduces to the ordinary stochastic quantization scheme on large scales, but it also opens up interesting new perspectives: chaotic strings appear to minimize their vacuum energy for the observed numerical values of the free standard model parameters.
Preface vii
Introduction xiii
Chaotic quantization of field theories
1(26)
Stochastic quantization
1(2)
Dynamical generation of the noise
3(3)
The free Klein-Gordon field with chaotic noise
6(3)
Chaotic quantization in momentum space
9(2)
Gauge fields with chaotic noise
11(2)
Distinguished properties of Tchebyscheff maps
13(4)
Graph theoretical method
17(6)
Perturbative approach
23(4)
Chaotic strings
27(30)
Motivation for chaotic strings
27(3)
Anti-integrable limit of a continuum φN+1-theory
30(3)
Possible generalizations
33(2)
Yet another way to derive the chaotic string
35(3)
Symmetry properties
38(3)
Stability properties
41(3)
Fixed points
44(3)
Spatio-temporal patterns
47(10)
Vacuum energy of chaotic strings
57(18)
Self energy of the N = 3 string
57(3)
Self energy of the N = 2 string
60(2)
Self energy for general N
62(3)
Interaction energy of chaotic strings
65(2)
Double strings
67(2)
Rotating strings
69(6)
Phase transitions and spontaneous symmetry breaking
75(20)
Some general remarks on phase transitions
75(4)
Vacuum expectation on 1-dimensional lattices
79(3)
Real scalar field on d-dimensional lattices
82(8)
Complex scalar field with U(1) symmetry
90(2)
Chaotic Higgs field with SU(2) symmetry
92(3)
Stochastic interpretation of the uncertainty relation
95(18)
Fluctuations of momenta and positions
95(2)
Newton's law and self interaction
97(2)
Coulomb forces and Laplacian coupling
99(4)
Duality of interpretations
103(1)
Feynman webs
104(2)
Physical interpretation of discrete string symmetries
106(2)
Fluctuations of the metric and a 1+1 dimensional model of quantum gravity
108(5)
Generalized statistical mechanics approach
113(18)
Heat bath of the vacuum
113(3)
States of maximum information
116(2)
States of minimum correlation
118(1)
Nonextensive Statistical mechanics
119(5)
Energy dependence of the entropic index q
124(2)
Fluctuations of temperature
126(3)
Klein-Gordon field with fluctuating momenta
129(2)
Interaction energy of chaotic strings
131(20)
Analogue of the Einstein field equations
131(2)
The 3A string---electric interaction strengths of electrons and d-quarks
133(3)
The 3B string---weak interaction strengths of neutrinos and u-quarks
136(3)
High-precision prediction of the electroweak parameters
139(2)
The 2A string---strong interaction strength at the W-mass scale
141(3)
The 2B string---the lightest scalar glueball
144(1)
The 2A - and 2B- strings --- towards a Higgs mass prediction
145(3)
Gravitational interaction
148(3)
Self energy of chaotic strings
151(24)
Self interacting scalar field equations
151(1)
The 3A string -weak and strong interactions of heavy fermion flavors
152(4)
The 3B string - further mixed states of heavy fermion flavors
156(2)
The 2A string - further bosons
158(2)
The 2B string - Yukawa interaction of the top quark
160(2)
Yukawa and gravitational interactions of all quarks and leptons
162(6)
Neutrino mass prediction
168(4)
The 2A- and 2B- strings - bosonic mass ratios
172(3)
Total vacuum energy of chaotic strings
175(16)
Hadronization of free quarks
175(4)
Mesonic states
179(3)
Baryonic states
182(4)
CP violation
186(1)
Planck scale interpretation
186(1)
Dark matter
187(4)
Grand unification
191(16)
Supersymmetric versus non-supersymmetric theories
191(3)
A supersymmetric scenario
194(2)
A non-supersymmetric scenario
196(2)
Final unification at the Planck scale
198(2)
Simplification for sin2 θW = 1/2
200(2)
Bosons at the Planck scale
202(1)
Some thoughts on supersymmetry
203(4)
11-dimensional space-time and quantum gravity
207(22)
Chaotic dynamics in compactified dimensions
207(3)
Quantized Einstein field equations
210(3)
N = 1 strings and Minkowski space
213(2)
Potentials for the N = 1 strings and inflation
215(2)
Black holes, Hawking radiation, and duality
217(3)
The limit E → ∞
220(2)
Brief history of the universe - as seen from chaotic strings
222(7)
Summary
229(24)
Motivation and main results
229(3)
The chaotic string dynamics
232(2)
Vacuum energy of chaotic strings
234(3)
Fixing standard model parameters
237(3)
Numerical findings
240(7)
Physical embedding
247(2)
Conclusion
249(4)
Bibliography 253(14)
Index 267


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