Gauge transformation in Einstein–Yang–Mills theories
We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent whe...
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Veröffentlicht in: | Journal of mathematical physics 2000-08, Vol.41 (8), p.5557-5571 |
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creator | Pons, J. M. Salisbury, D. C. Shepley, L. C. |
description | We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure Yang–Mills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the space–time metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer. |
doi_str_mv | 10.1063/1.533425 |
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M.</creatorcontrib><creatorcontrib>Salisbury, D. C.</creatorcontrib><creatorcontrib>Shepley, L. C.</creatorcontrib><title>Gauge transformation in Einstein–Yang–Mills theories</title><title>Journal of mathematical physics</title><description>We discuss the relation between space–time diffeomorphisms and gauge transformations in theories of the Yang–Mills type coupled with Einstein’s general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure Yang–Mills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the space–time metric plus associated gauge transformations. 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title | Gauge transformation in Einstein–Yang–Mills theories |
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