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Is the principle of least action a must?

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)