Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-11-23
Nucl.Phys. B421 (1994) 391-412
Physics
High Energy Physics
High Energy Physics - Theory
26 pages, plain TeX; UBCTP 93-011
Scientific paper
10.1016/0550-3213(94)90333-6
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the associated path integrals can be applied. We show that in the case of a maximally symmetric phase space the only applicable Hamiltonians are essentially harmonic oscillators, while for non-homogeneous phase spaces the possibilities are more numerous but ambiguities in the path integrals occur. In the latter case we give general formulas for the Darboux Hamiltonians, as well as the Hamiltonians which result naturally from a generalized coherent state formulation of the quantum theory which shows that again the Hamiltonians so obtained are just generalized versions of harmonic oscillators. Our analysis and results describe the quantum geometry of some two dimensional systems.
Semenoff Gordon W.
Szabo Richard J.
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