Field Redefinitions in Classical Field Theory with some Quantum Perspectives

TL;DR

This paper explores classical field redefinitions, emphasizing the importance of observable choices and initial conditions, and discusses their implications for both classical and quantum field theories, including non-invertible redefinitions.

Contribution

It provides a classical analogue to the LSZ formula and analyzes the limitations of non-invertible redefinitions, bridging classical and quantum perspectives.

Findings

Classical analogue to LSZ formula confirms observable invariance

Non-invertible redefinitions affect soliton solutions

Proper observable selection ensures physical invariance

Abstract

In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the choice of observables, the range of applicability, and the appearance and disappearance of solutions of the equations of motion (EOM). Many of these issues can already be studied at the classical level, which is the focus of this work. We highlight the importance of selecting appropriate observables and initial/boundary conditions to ensure the physical invariance of solutions. A classical analogue to the Lehmann-Symanzik-Zimmermann (LSZ) formula is presented, confirming that some observables remain independent of field variables without tracking redefinitions. Additionally, we address, with an example, the limitations of non-invertible field redefinitions, particularly with non-perturbative objects like solitons, and discuss their implications for classical and quantum field theories.