Field Redefinition Invariance and "Extra Terms"

TL;DR

This paper explores how nonlinear coordinate transformations affect discretized quantum path integrals, deriving additional terms in the action and discussing their relation to renormalization group procedures and field theory redefinitions.

Contribution

It provides the first complete derivation of extra terms arising from nonlinear transformations in discretized quantum mechanics and links these to renormalization concepts.

Findings

Derived explicit form of extra terms in discretized path integrals.

Connected extra terms to renormalization group blocking procedures.

Applied field redefinition analysis to a 2D field theory.

Abstract

We investigate the issue of coordinate redefinition invariance by carefully performing nonlinear transformations in the discretized quantum mechanical path integral. By resorting to hamiltonian path integral methods, we provide the first complete derivation of the extra terms (beyond the usual jacobian term) which arises in the action when a nonlinear transformation is made. We comment on possible connections with the renormalization group, by showing that these extra terms may emerge from a ``blocking" procedure. Finally, by performing field redefinitions before and after dimensional reduction of a two dimensional field theory, we derive an explicit form fo an extra term appearing in a field theory.