Quantum-classical interactions through the path integral

Abstract

I consider the case of two interacting scalar fields, ϕand ψ, and use the path integral formalism in order to treat the first classically and the second quantum-mechanically. I derive the Feynman rules and the resulting equation of motion for the classical field, which should be an improvement of the usual semi-classical procedure. As an application I use this method in order to enforce Gauss's law as a classical equation in a non-abelian gauge theory. I argue that the theory is renormalizable and equivalent to the usual Yang-Mills as far as the gauge field terms are concerned. There are additional terms in the effective action that depend on the Lagrange multiplier field λthat is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.

16 pages, LaTeX, 1 fig, final version to appear in PRD

References in corpus (8)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Constituent Quarks from QCD
• On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
• Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
• The Boltzmann Equation in Classical and Quantum Field Theory
• Perturbative Confinement
• Split Dimensional Regularization for the Coulomb Gauge
• Perturbation theory via Feynman diagrams in classical mechanics

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