Complete treatment of effective actions within the Gaussian approximation and systematic generalizations

Publisher Website
Google Scholar
Abstract
The Gaussian approximation is generalized to include the complete effective action with arbitrary inhomogeneous background fields. This offers new possibilities to treat static and dynamical solitons resigning semiclassical approximation schemes. The analytical continuation to imaginary time allows us to deal with nonclassical instantons. Our procedure is based on time-dependent variational methods of which at least one concept can be extended to a post-Gaussian approximation nonperturbatively. We construct a unique mapping between a quantum field theory of a scalar field in 1+1 dimensions and a classical field theory of an infinite number of local and multilocal fields. As an application we treat the sine-Gordon system. A preliminary comparison of our numerical results with a semiclassical calculation of the soliton mass is presented and will be extended in a forthcoming publication.