1303.3179 (Masao Matsumoto)

Restriction on Types of Coherent States due to Gauge Symmetry    [PDF]

Masao Matsumoto

From the viewpoint of the formulation of the SU(2) coherent states and their path integrals labeled by a full set of Euler angles (\phi, \theta, \psi) which we developed in the previous paper, we study the relations between gauge symmetries of Lagrangians and allowed quantum states; We investigate permissible types of fiducial vectors in the full quantum dynamics in terms of SU(2) coherent states. We propose a general framework for a Lagrangian having a certain gauge symmetry with respect to one of the Euler angles \psi. We find that when a Lagrangian has the gauge symmetry fiducial vectors are so restricted that they belong to the eigenstates of ${\hat S}_3$ or to the orbits of them under the action of the SU(2); And the strength of a fictitious monopole, which appears in the Lagrangian, is a multiple of 1 / 2. In this case Dirac strings are permitted. One exceptional case exists when the fictitious monopole charge disappears. The reasoning here does not work for a Lagrangian without the gauge symmetry. The relations between formulations and results of the preceding work by Stone that has piloted us and those by ours are also discussed.

View original: http://arxiv.org/abs/1303.3179