Projective Quantum Mechanics

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dc.creatorIsidro, J. M.
dc.date2003-04-21
dc.date.accessioned2026-07-07T04:15:10Z
dc.date.available2026-07-07T04:15:10Z
dc.descriptionWe study the quantisation of complex, finite-dimensional, compact, classical phase spaces C, by explicitly constructing Hilbert-space vector bundles over C. We find that these vector bundles split as the direct sum of two holomorphic vector bundles: the holomorphic tangent bundle T(C), plus a complex line bundle N(C). Quantum states (except the vacuum) appear as tangent vectors to C. The vacuum state appears as the fibrewise generator of N(C). Holomorphic line bundles N(C) are classified by the elements of Pic(C), the Picard group of C. In this way Pic(C) appears as the parameter space for nonequivalent vacua. Our analysis is modelled on, but not limited to, the case when C is complex projective space.
dc.description16 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/hep-th/0304175
dc.identifierhttp://arxiv.org/abs/hep-th/0304175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51902
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleProjective Quantum Mechanics
dc.typetext

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