The Background Field Method as a Canonical Transformation

Details The Background Field Method as a Canonical Transformation The Background Field Method as a Canonical Transformation

2012-03-29

arxiv.org/abs/1203.6637v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, REVTeX

Scientific paper

We construct explicitly the canonical transformation that controls the full dependence (local and non-local) of the vertex functional of a Yang-Mills theory on a background field. After showing that the canonical transformation found is nothing but a direct field-theoretic generalization of the Lie transform of classical analytical mechanics, we comment on a number of possible applications, and in particular the non perturbative implementation of the background field method on the lattice, the background field formulation of the two particle irreducible formalism, and, finally, the formulation of the Schwinger-Dyson series in the presence of topologically non-trivial configurations.

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