On Local Variational Differential Operators in Field Theory

TL;DR

This paper introduces a new calculus for local variational differential operators that avoids indefinite quantities and applies it to gauge field theories, enhancing the mathematical framework of field theory.

Contribution

The paper develops a novel calculus for local variational operators, improving upon canonical calculus by eliminating indefinite quantities and applying it to gauge theories.

Findings

New calculus for local variational operators developed

Application to BV and Sp(2)-symmetric gauge theories demonstrated

Relation to quasiclassical expansion discussed

Abstract

We propose and develop a new calculus for local variational differential operators. The main difference of the new formalism with the canonical differential calculus is that the image of higher order operators on local functionals does not contain indefinite quantities like $\delta(0)$. We apply this formalism to BV formulation of general gauge field theory and to its Sp(2)-symmetric generalization. Its relation to a quasiclassical expansion is also discussed.