Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory

TL;DR

This paper extends Noether's theorem to non-Lagrangian field theories using the Lagrange anchor, enabling the identification of conservation laws without relying on variational principles.

Contribution

It introduces a method to derive conservation laws in non-Lagrangian theories via the Lagrange anchor, broadening the scope of symmetry-conservation relationships.

Findings

Extended Noether theorem to non-Lagrangian theories

Demonstrated quantization of non-Lagrangian fields using Lagrange anchor

Identified new conservation laws in non-variational dynamics

Abstract

Making use of the Lagrange anchor construction introduced earlier to quantize non-Lagrangian field theories, we extend the Noether theorem beyond the class of variational dynamics.