Abstract
A path-integral formulation in the representation of coherent states for the unitary U2 group and U2/1 supergroup is introduced. U2 and U2/1 path integrals are shown to be defined on the coset spaces U2/U1(X)U1 and U2/1/U1/1(X)U1 respectively. These cosets appear as curved classical phase spaces. Partition functions are expressed as path integrals over these spaces. In the case when U2 and U2/1 are the dynamical groups, the corresponding path integrals are evaluated with the help of linear fractional transformations that appear as the group (supergroup) action in the coset space (superspace). Possible applications for quantum models are discussed.
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