Is the principle of least action a must?

TL;DR

This paper questions the fundamental necessity of the least action principle in classical field theories, demonstrating that field equations can be derived from symmetries and conservation laws without it.

Contribution

It shows through examples that classical field equations can be obtained without relying on the least action principle, challenging its assumed central role.

Findings

Field equations derived from symmetries and conservation laws

Least action principle not always essential in classical field theory

Examples include three detailed classical interacting field theories

Abstract

The least action principle occupies a central part in contemporary physics. Yet, as far as classical field theory is concerned, it may not be as essential as generally thought. We show with three detailed examples of classical interacting field theories that it is possible, in cases of physical interest, to derive the correct field equations for all fields from the action (which we regard as defining the theory), some of its symmetries, and the conservation law of energy-momentum (this last regarded as ultimately coming from experiment)