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arXiv:hep-ph/9806343

Classical fields as coherent states and diffusion equations

Jukka Sirkka, Iiro Vilja

Published Jun 11, 1998• 0 citations
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Abstract

We present a derivation of the effect of the classical field configuration to the diffusion equations. Using the formalism of the thermo field dynamics we propose a systematic and consistent way to treat the classical background and to calculate it's effect at any order of the perturbation theory. We treat the classical field in genuine quantum field theory formalism as a coherent state and show how the propagators and self energies are altered in this case.

DOI
10.48550/arxiv.hep-ph/9806343

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We present a derivation of the effect of the classical field configuration to the diffusion equations. Using the formalism of the thermo field dynamics we propose a systematic and consistent way to treat the classical background and to calculate it's effect at any order of the perturbation theory. We treat the classical field in genuine quantum field theory formalism as a coherent state and show how the propagators and self energies are altered in this case.
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Abstract A new formalism is introduced to treat problems in quantum field theory, using coherent functional expansions rather than path integrals. The basic results and identities of this approach are developed. In the case of a Bose gas with point-contact interactions, this leads to a soluble functional equation in the weak interaction limit, where the perturbing term is part of the kinetic energy. This approach has the potential to prevent the Dyson problem of divergence in perturbation theory.
We develop a coherent-field formulation of quantum electrodynamics (QED) based on coherent-state boundary conditions, in which laser fields are represented by asymptotic coherent states rather than by prescribed classical background fields. Starting from coherent-state boundary conditions and the displacement-operator formalism, we construct operator and path-integral descriptions of transitions between distinct electromagnetic coherent states. This formulation provides a coherent-field extension of conventional background-field QED and incorporates the quantum dynamics of the coherent field itself. The corresponding path-integral representation contains a functional integral over coherent-field histories in addition to the usual functional integral over quantum fluctuations, thereby extending the conventional background-field description. The resulting path-integral representation naturally leads to an effective action for the stationary coherent-field configuration. The corresponding saddle-point condition yields an effective Maxwell equation containing contributions from vacuum polarization, photon fluctuations, and coherent-field fluctuations. In the limit where the latter two contributions vanish, the formalism reduces to the conventional Heisenberg-Euler description.