Abelian gerbes as a gauge theory of quantum mechanics on phase space

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dc.creatorIsidro, J. M.
dc.creatorde Gosson, M. A.
dc.date2006-08-14
dc.date.accessioned2026-07-07T11:07:02Z
dc.date.available2026-07-07T11:07:02Z
dc.descriptionWe construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB. All three of them are defined exclusively in terms of elements already present in P, the only external input being Planck's constant h. U(1) gauge transformations acting on the triple A,B,H are also defined, parametrised either by a 0-form or by a 1-form. While H remains gauge invariant in all cases, quantumness vs. classicality appears as a choice of 0-form gauge for the 1-form A. The fact that [H]/2iπis an integral class in de Rham cohomology is related with the discretisation of symplectic area on P. This is an equivalent, coordinate-free reexpression of Heisenberg's uncertainty principle. A choice of 1-form gauge for the 2-form B relates our construction with generalised complex structures on classical phase space. Altogether this allows one to interpret the quantum mechanics corresponding to P as an Abelian gauge theory.
dc.description18 pages, 1 figure available from the authors upon request
dc.identifierhttps://arxiv.org/abs/hep-th/0608087
dc.identifierhttp://arxiv.org/abs/hep-th/0608087
dc.identifierJ.Phys.A40:3549-3568,2007
dc.identifierdoi:10.1088/1751-8113/40/13/016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/189715
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleAbelian gerbes as a gauge theory of quantum mechanics on phase space
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