Physics – Quantum Physics
Scientific paper
2012-01-25
Physics
Quantum Physics
LaTex 2e with IOP class file; It may be replaced by a usual LaTex file. The augmented version of the formulation part of quant
Scientific paper
We develop the formulation of the spin (SU(2)) coherent state path integrals based on arbitrary fiducial vectors. The coherent state, which is defined on a 3-sphere, is specified by a full set of Euler angles. We obtain the time evolution in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term `a la Balachandran et al as well as some additional terms, both of which depend on the vectors in a simple way. Semiclassical equations for parameters of the coherent states are also given. In this paper we concentrate on the basic formulation. The process of the discrete path integrals to the continuous ones is clarified. It is shown that the fictitious gauge potential is non-singular as in the Balachandran case. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to monopoles and geometric phases, will be treated in subsequent papers separately.
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