Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-18
Mod.Phys.Lett. A9 (1994) 2705-2718
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, Plain TeX; UBCTP-94-005
Scientific paper
We study equivariant localization formulas for phase space path integrals when the phase space is a multiply connected compact Riemann surface. We consider the Hamiltonian systems to which the localization formulas are applicable and show that the localized partition function for such systems is a topological invariant which represents the non-trivial homology classes of the phase space. We explicitly construct the coherent states in the canonical quantum theory and show that the Hilbert space is finite dimensional with the wavefunctions carrying a projective representation of the discrete homology group of the phase space. The corresponding coherent state path integral then describes the quantum dynamics of a novel spin system given by the quantization of a non-symmetric coadjoint Lie group orbit. We also briefly discuss the geometric structure of these quantum systems.
Semenoff Gordon W.
Szabo Richard J.
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