Symmetric Criticality in Classical Field Theory

Abstract

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler‐Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group‐invariant Lagrangian by the symmetry group yields the correct symmetry‐reduced Euler‐Lagrange equations.