Symmetries, Conservation Laws, and Variational Principles for VectorField Theories
Proceedings of the Cambridge Philisophical Society
The interplay between symmetries, conservation laws, and variational principles is a rich and varied one and extends well beyond the classical Noether's theorem. Recall that Noether's first theorem asserts that to every r dimensional Lie algebra of (generalized) symmetries of a variational problem there are r conserved quantities for the corresponding Euler-Lagrange equations. Noether's second theorem asserts that infinite dimensional symmetry algebras (depending upon arbitrary functions of all the independent variables) lead to differential identities for the Euler-Lagrange equations.
Symmetries, Conservation Laws, and Variational Principles for Vector Field Theories (with J. Pohjanpelto), Proc. Camb. Phil. Soc. 120 (1996) 369–384.