Do all identically conserved geometric tensors come from actions? A status report

Abstract

Noether's theorem, that local gauge variations of gauge invariant actions are identically conserved (more tautologically, that gauge variations of gauge invariants vanish) was established a century ago. Its converse, in the geometric context: are all identically conserved local symmetric tensors variations of some coordinate invariant action? remains unsolved to this day. We survey its present state and discuss some of our concrete attempts at a solution, including a significant improvement. For notational simplicity, details are primarily given in $D=2$, but we discuss generic $D$ as well.

Published version

References in corpus (3)

• Minimal Massive 3D Gravity
• Is the principle of least action a must?
• Non-Lagrangian Gauge Field Models are Physically Excluded

Cited by in corpus (3)

• Energy of asymptotically AdS black holes in Exotic Massive Gravity and its log-extension
• Non-Lagrangian Gauge Field Models are Physically Excluded
• Noether Converse: all identically conserved geometric tensors are metric variations of an action in (at least) D = 2