Symmetries and conservation laws

The first-variation identity, both Noether theorems and their converses, mechanics and gauge fields, the stationary black-hole first law, null Lagrangians, Euler covariance, the reduction of Riemannian differential invariants to curvature, and Lie–Tresse differential generation on one finite-level invariant domain for regular Cartan jet actions.

1. Variational symmetries and Noether's first theorem
2. Infinite symmetry groups and Noether's second theorem
3. The formal calculus of variations and differential invariants

Original text CC0 1.0 unless the lesson states other terms.