Hamiltonian facets of classical gauge theories on E-manifolds
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hdl:2117/376985
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Data publicació2022-09-21
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Abstract
Manifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in [NT01] and investigated in depth in [MS20]. In this article we explore their physical facets by extending gauge theories to the E-category. Singularities in the configuration space of a classical particle can be described in several new scenarios unveiling their Hamiltonian aspects on an E-symplectic manifold. Following the scheme inaugurated in [Wei78], we show the existence of a universal model for a particle interacting with an E-gauge field. In addition, we generalize the description of phase spaces in Yang-Mills theory as Poisson manifolds and their minimal coupling procedure, as shown in [Mon86], for base manifolds endowed with an E-structure. In particular, the reduction at coadjoint orbits and the shifting trick are extended to this framework. We show that Wong's equations, which describe the interaction of a particle with a Yang-Mills field, become Hamiltonian in the E-setting. We formulate the electromagnetic gauge in a Minkowski space relating it to the proper time foliation and we see that our main theorem describes the minimal coupling in physical models such as the compactified black hole.
CitacióMir, P.; Miranda, E.; Nicolás, P. Hamiltonian facets of classical gauge theories on E-manifolds. 2022.
Altres identificadorshttps://arxiv.org/abs/2209.10653
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2209.10653drac.pdf | Article principal a ArXiV | 748,7Kb | Visualitza/Obre |