Semiclassical propagation of spin-coherent states (7 pages)

Marcel Novaes, Marcus A. M. de Aguiar

Jens Bolte

Rafał Demkowicz-Dobrzański

Michael Stone, W. Green St

We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the “extra phase ” discovered by Solari and Kochetov, and show that this correction is related to an anomaly in the fluctuation determinant. We show that, once this extra factor is included, the semiclassical propagator has the correct short time behaviour to O(T 2), and demonstrate its consistency under dissection of the path.

Mikhail Pletyukhov

The problem of an origin of the Solary-Kochetov extra-phase contribution to the naive semiclassical form of a generalized phase-space propagator is addressed with the special reference to the su(2) spin case which is the most important in applications. While the extra-phase correction to a flat phase-space propagator can straightforwardly be shown to appear as a difference between the principal and the Weyl symbols of a Hamiltonian in the next-to-leading order expansion in the semiclassical parameter, the same statement for the semiclassical spin coherent-state propagator holds provided the Holstein-Primakoff representation of the su(2) algebra generators is employed.

George A. Hagedorn