Quantum-classical interactions through the path integral

Details Quantum-classical interactions through the path integral Quantum-classical interactions through the path integral

2006-07-26

arxiv.org/abs/hep-th/0607210v6

Phys.Rev.D75:065023,2007

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.75.065023

I consider the case of two interacting scalar fields, \phi and \psi, 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 \lambda that is used to enforce the constraint. These terms and their relation to the confining properties of the theory are discussed.

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