Massive to Massless by Applying a Nonlocal Field Redefinition

TL;DR

This paper demonstrates how nonlocal field redefinitions can transform massive theories into massless ones and vice versa, challenging the usual invariance of physical observables under local redefinitions.

Contribution

It introduces explicit invertible nonlocal field redefinitions that change the physical mass spectrum of theories, providing new insights into field theory transformations.

Findings

Nonlocal redefinitions can eliminate or introduce mass in theories.

Explicit examples include harmonic oscillator, scalar, and Dirac fields.

Physical observables like mass are not invariant under nonlocal redefinitions.

Abstract

The invariance of physical observables like particle's mass under a local field redefinition is a well-known and important property of quantum field theory. In this paper, on the other hand, we investigate nonlocal field redefinitions eliminating a physical observable from a theory. Indeed, by giving explicit examples, we present invertible nonlocal field redefinitions reducing a massive theory to the massless one, and vice versa. The studied examples are: classical harmonic oscillator, the scalar field theory, and the Dirac field theory.