1201.5258 (Masao Matsumoto)

SU(2) coherent state path integrals labelled by a full set of Euler
angles: basic formulation    [PDF]

Masao Matsumoto

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.

View original: http://arxiv.org/abs/1201.5258