Quantum fields in disequilibrium: Neutral scalar bosons with long-range, inhomogeneous perturbations

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Abstract
Using Schwinger’s quantum action principle, dispersion relations are obtained for neutral scalar mesons interacitng with bilocal sources. These relations are used as the basis of a method for representing the effect of interactions in the Gaussian approximation to field theory, and it is argued that a marked inhomogeneity, in space-time dependence of the sources, forces a discrete spectrum on the field. The development of such a system exhibits features commonly associated with chaos and self-organization (localization by domain or cell formation). The Green functions play the role of an iterative map in phase space. Stable systems reside at the fixed points of the map. The present work can be applied to self-interacting theories by choosing suitable properties for the sources. Rapid transport leads to a second-order phase transition and anomalous dispersion. Finally, it is shown that there is a compact representation of the nonequilibrium dynamics in terms of generalized chemical potentials, or equivalently as a pseudogauge theory, with an imaginary charge. This analogy shows, more clearly, how dissipation and entropy production are related to the source picture and transform a flip-flop like behavior between two reservoirs into the Landau problem in a constant ‘‘magnetic field.’’ A summary of conventions and formalism is provided as a basis for future work. © 1995 The American Physical Society.
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