Spatio-temporal Chaos and Vacuum Fluctuations of Quantized Fields
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.
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Vacuum energy of chaotic strings
Phase transitions and spontaneous symmetry break
Stochastic interpretation of the uncertainty rela
Generalized statistical mechanics approach
Interaction energy of chaotic strings
Self energy of chaotic strings
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1-dimensional 3B string backward coupling baryons Beck behaviour black holes chaotic dynamics chaotic noise chaotic string dynamics chaotic string theories chaotic strings chapter coincide compactified compactified space corresponding coupled map lattices coupling constant coupling form described diffusive coupling electroweak energy scale evolve expectation fermion masses Feynman web interpretation fictitious field equation field theories formally Gaussian white noise given glueball gravitational coupling Hence Higgs invariant density iterates leptons Lett M-theory mass scales mesons metric minima minimum mixing angle momentum neutrino noise fields numerical observed obtain ordinary Parisi-Wu approach particles phase transition Phys physical interpretation Planck scale potential precision prediction quark masses relevant self-interacting sin2 space-time spatial spatio-temporal spin stable zeros standard model couplings standard model parameters statistical mechanics stochastic quantization string theories strong coupling superstring theory supersymmetric symmetry Tchebyscheff maps temperature thermodynamic Tsallis vacuum energy vacuum fluctuations virtual particles Wiener process yields