Killing Symmetries as Hamiltonian Constraints

TL;DR

This paper explores how Killing symmetries in gauge theories correspond to additional Hamiltonian constraints, affecting physical degrees of freedom and gauge freedom, with implications for electromagnetism and gravity.

Contribution

It establishes a formal connection between Killing symmetries and Hamiltonian constraints, clarifying their impact on gauge theories and physical observables.

Findings

Time-like Killing vectors restrict electromagnetic fields to pure gauge configurations.

In ADM gravity, time-like Killing vectors eliminate gravitational waves, leaving only inertial effects.

Killing symmetries impose constraints that shape the physical phase space in gauge theories.

Abstract

The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time , while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.