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Schlagwörter:
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Zusammenfassung:
We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space {\bb 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 {\bb P} , the only external input being Planck's constant planck. U(1) gauge transformations acting on the triple A, B, H are also defined, parametrized either by a 0-form or by a 1-form. While H remains gauge invariant in all cases, quantumness versus classicality appears as a choice of 0-form gauge for the 1-form A. The fact that [H]/2πi is an integral class in de Rham cohomology is related to the discretization of symplectic area on {\bb 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 to generalized complex structures on classical phase space. Altogether this allows one to interpret the quantum mechanics corresponding to {\bb P} as an Abelian gauge theory.
