Field Redefinitions Can Be Nonlocal

TL;DR

This paper demonstrates that field redefinitions in quantum field theory can be nonlocal, symmetry-breaking, and spacetime-dependent, with implications for perturbation theory and multiparticle soft theorems.

Contribution

It shows that there are essentially no restrictions on field redefinitions, including nonlocal and symmetry-breaking ones, across all orders in perturbation theory and for any dispersion relation.

Findings

Field redefinitions can be nonlocal and spacetime-dependent.

Resummation of redefinitions into propagators is possible.

Derived higher-order Schwinger-Dyson equations and multiparticle soft theorems.

Abstract

We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions can be nonlocal, symmetry breaking, or in certain cases have explicit dependence on spacetime. We address field redefinitions that can be resummed into the propagator, which demonstrates how to perform perturbative calculations away from the minimum in field space. Field redefinitions are used to derive higher-order Schwinger-Dyson equations, which imply multiparticle soft theorems. Non-standard field redefinitions are showcased using both relativistic and nonrelativistic examples.