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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Path integrals over the SU(2) manifold and related potentials

I. H. Duru

Published Nov 15, 1984• 41 citations
Publisher

Abstract

A path-integral formalism is developed on the SU(2) manifold parametrized in terms of the Euler angles. The Green's function is studied for the P"oschl-Teller potential and the corresponding wave functions and energy spectrum are obtained.
DOI
10.1103/physrevd.30.2121

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We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term à la Balachandran et al. as well as some additional terms, both of which depend on fiducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.
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