Multicomponent WKB and Quantization

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dc.creatorEmmrich, C.
dc.creatorRömer, H.
dc.date1996-01-25
dc.date.accessioned2026-07-07T04:21:50Z
dc.date.available2026-07-07T04:21:50Z
dc.descriptionHamiltonians whose symbols are not simply real valued, but matrix or, more generally, endomorphism valued functions appear in many places in physics, examples being the Dirac equation, multicomponent wave equations like electrodynamics in media, and Yang-Mills theories, and the Born-Oppenheimer approximation in molecular physics. The aim of this paper is to give a completely geometric approach to the WKB approximation od such systems, and to reduce the problem ``as far as possible'' to the scalar case. A star-product formulation of quantum mechanics proves to be particularly useful in this context. As opposed to other approaches in the literature which restrict themselves to the use of the Moyal product and thus to the study of trivial bundles (or local trivializations) over $\real^{2n}$, we will consider general bundles over arbitrary symplectic manifolds. Here, Fedosov's construction \cite{fedosov} will be the adequate tool, since it gives an explicit construction for star products in this general setting.
dc.description10 pages, latex
dc.identifierhttps://arxiv.org/abs/hep-th/9601138
dc.identifierhttp://arxiv.org/abs/hep-th/9601138
dc.identifierActa Phys.Polon. B27 (1996) 2393-2402
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/54483
dc.subjectHigh Energy Physics - Theory
dc.titleMulticomponent WKB and Quantization
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