Killing symmetries as Hamiltonian constraints. (English) Zbl 1339.83022
Summary: 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.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 83C35 | Gravitational waves |
| 83C22 | Einstein-Maxwell equations |
| 83C40 | Gravitational energy and conservation laws; groups of motions |
| 78A25 | Electromagnetic theory (general) |
| 83A05 | Special relativity |
| 70H20 | Hamilton-Jacobi equations in mechanics |
Keywords:
canonical gravity; Killing symmetries; Hamiltonian constraints; gauge theory; gauge freedom; electromagnetic fields; Maxwell theory; Minkowski space-time; ADM canonical gravity; gravitational wavesReferences:
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