Path integral in the representation of SU(2) coherent state and classical dynamics in a generalized phase space

Abstract

Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.

The semiclassical coherent state propagator for systems with spin

“…Approximations for spin coherent states have also been studied by Kuratsuji and Suzuki [20]. The basic difference between their approach and Klauder's is that the later represents the classical trajectories in a Bloch sphere by means of angle variables while Kuratsuji and Suzuki represents the same dynamics in terms of an stereographic projection of the Bloch sphere on a complex plane.…”

Semiclassical theory of spin orbit interaction in the extended phase space

“…The path integral for a system with spin in the SU(2) spin-coherent-state representation originally appeared in a paper by Klauder [21] as an integral on the sphere S 2 . Kuratsuji et al [23] have represented it as an integral over paths in the extended complex planeC 1 .…”

The semiclassical propagator for spin coherent states

“…The inner product of two of these states is 2) and the left eigenstates j, m| ofĴ 2 andĴ 3 have coherent-state wavefunctions…”

“…Coherent-state path integrals for spin were introduced by Klauder [1], and by Kuratsuji and Suzuki [2]. Related phase space path integrals were introduced by Jevicki and Papanicolaou [3], and by Nielsen and Röhrlich [4].…”