Chaos and Gauge Field Theory

Bı́ró, Tamás; Matinyan, S.G.; Müller, Berndt

doi:10.1142/9789812798978

Cited by 72 publications

(145 citation statements)

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“…This chaotic behavior is a new effect not present in any classical treatment. It is generally well known that chaos plays an important role in general relativity [11], quantum field theories [12,13,14], and string theories [15]. The main result of our consideration is that the chaotic field theories considered naturally generate a small cosmological constant and have the scope to offer simultaneous solutions to the cosmological coincidence and uniqueness problem.…”

Section: Introductionmentioning

confidence: 90%

Chaotic scalar fields as models for dark energy

Beck

2004

Phys. Rev. D

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We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena if the self interaction strength is strong. The stochastically quantized dynamics can degenerate to a chaotic dynamics conjugated to a Bernoulli shift in fictitious time, and the right amount of vacuum energy density can be generated without fine tuning. It is numerically observed that the scalar field dynamics distinguishes fundamental parameters such as the electroweak and strong coupling constants as corresponding to local minima in the dark energy landscape. Chaotic fields can offer possible solutions to the cosmological coincidence problem, as well as to the problem of uniqueness of vacua.

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Section: Introductionmentioning

confidence: 90%

Chaotic scalar fields as models for dark energy

Beck

2004

Phys. Rev. D

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“…This also opens up for a treatment of "measurement" in quantum field theory. As a nonlinear gauge evolution is effectively non-reversible, especially if chaotic [5], it lies close to identify it with the physical "mechanism" of the "irreversible amplification" emphasized by Bohr as being necessary to produce classical, observable results from the quantum mechanical formalism. Even though Bohr himself denounced the need, or even the possibility, to give a physical description of this "mechanism" [20], we believe that the central issue for truly understanding quantum mechanics lies in the quantum measurement problem.…”

Section: Implementation (Rough)mentioning

confidence: 92%

“…We, on the other hand, propose that the nonlinearity in the underlying dynamics could be responsible for the seemingly random character of quantum mechanics. This is possible as it is well known that classical gauge field theories can be chaotic [5] (in which case no analytic, closed formula solutions exist, seemingly precluding any simple "quantization recipe"). In "usual", nonrelativistic quantum chaos the nonlinearities would merely introduce higher order terms in the operator potentials in the Hamiltonian.…”

Section: Ideamentioning

confidence: 99%

Nonlinear gauge interactions: A possible solution to the “measurement problem” in quantum mechanics

Hansson¹

2010

Physics Essays

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Two fundamental, and unsolved problems in physics are: i) the resolution of the "measurement problem" in quantum mechanics ii) the quantization of strongly nonlinear (nonabelian) gauge theories. The aim of this paper is to suggest that these two problems might be linked, and that a mutual, simultaneous solution to both might exist.We propose that the mechanism responsible for the "collapse of the wave function" in quantum mechanics is the nonlinearities already present in the theory via nonabelian gauge interactions. Unlike all other models of spontaneous collapse, our proposal is, to the best of our knowledge, the only one which does not introduce any new elements into the theory. A possible experimental test of the model would be to compare the coherence lengths -here defined as the distance over which quantum mechanical superposition is still valid -for, e.g., electrons and photons in a double-slit experiment. The electrons should have a finite coherence length, while photons should have a much longer coherence length (in principle infinite, if gravity -a very weak effect indeed unless we approach the Planck scale -is ignored).

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“…Previous studies on chaos in field theory have mostly emphasized chaotic behavior in gauge theory models (for a review and additional references and applications, see [2]). In special, in homogeneous Yang-Mills-Higgs models we can reduce the system of classical equations of motion to ones analogous to those of nonlinear coupled oscillators, which is well known to exhibit chaotic motion.…”

Section: Introductionmentioning

confidence: 99%

Chaotic symmetry breaking and dissipative two-field dynamics

Ramos

Navarro

2000

Phys. Rev. D

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The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model parameters leading to symmetry breaking along one of the field directions, the symmetry broken vacua make the role of transitory strange attractors and the field trajectories in phase space are strongly chaotic. Chaos is quantified by means of the determination of the fractal dimension, which gives an invariant measure for chaotic behavior. Discussions concerning chaos and dissipation in the model and possible applications to related problems are given.

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Chaos and Gauge Field Theory

Cited by 72 publications

References 0 publications

Chaotic scalar fields as models for dark energy

Chaotic scalar fields as models for dark energy

Nonlinear gauge interactions: A possible solution to the “measurement problem” in quantum mechanics

Chaotic symmetry breaking and dissipative two-field dynamics

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