Field redefinition invariant Lagrange multiplier formalism

TL;DR

This paper introduces a novel Lagrange multiplier formalism that maintains invariance under field redefinitions by incorporating ghost-like fields, ensuring the cancellation of extra degrees of freedom and preserving the physical content of the theory.

Contribution

It proposes a field redefinition invariant LM formalism with ghost fields that cancel additional degrees of freedom, improving the consistency of the path integral approach.

Findings

Ghost fields restore invariance under field redefinitions.

Extra degrees of freedom from LM fields are canceled by ghost fields.

The formalism eliminates doubling of degrees of freedom.

Abstract

In this paper, we propose a field redefinition invariant Lagrange multiplier (LM) formalism in which new ghost-like fields, analogous to Lee-Yang ghosts, are introduced. These ghost fields are required to restore the field redefinition invariance of the standard path integral of the LM theory and, at the same time, to cancel the additional contributions due to the LM fields. We argue that the extra degrees of freedom in the standard LM formalism, coming from the LM fields, should cancel against the degrees of freedom of the ghost fields. Hence, in the field redefinition invariant formalism the doubling of degrees of freedom, associated with the LM fields, is absent.