Abstract
We construct explicitly the canonical transformation which controls the full dependence (local and nonlocal) 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 nonperturbative 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 nontrivial configurations.
- Received 29 March 2012
DOI:https://doi.org/10.1103/PhysRevD.85.121702
© 2012 American Physical Society