SU(2) coherent state path integrals labeled by a full set of Euler angles: basic formulation
Abstract
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 a la Balachandran etal. as well as some additional terms, both of which depend on fiuducial 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.
Cite
@article{arxiv.1201.5258,
title = {SU(2) coherent state path integrals labeled by a full set of Euler angles: basic formulation},
author = {Masao Matsumoto},
journal= {arXiv preprint arXiv:1201.5258},
year = {2013}
}
Comments
LaTex 2e; 28 pages. We rearrange the contents in such a way that one can grasp the whole results clearer than before by three theorems; All the appendices except one are incorporated into the body of the text. The contraction of the general SU(2) coherent state path integrals to those for the generic canonical coherent states is added. arXiv admin note: substantial text overlap with arXiv:quant-ph/9906100