2016/05/23 by Townsend, Paul K.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1605.07128
A simple proof of Noether's first theorem involves the promotion of a constant symmetry parameter ε to an arbitrary function of time, the Noether charge Q is then the coefficient of ε in the variation of the action. Here we examine the validity of this proof for Lagrangian mechanics with arbitrarily-high time derivatives, in which context "higher-level" analogs of Noether's theorem can be similarly proved, and "Noetherian charges" read off from, e.g. the coefficient of ε in the variation of the action. While Q=0 implies a restricted gauge invariance, unrestricted gauge invariance requires zero Noetherian charges too. Some illustrative examples are considered and the extension to field theory discussed.