Trace formula for systems with spin from the coherent state propagator

We present a detailed derivation of the trace formula for a general Hamiltonian with two degrees of freedom where one of them is canonical and the other a spin. Our derivation starts from the semiclassical formula for the propagator in a basis formed by the product of a canonical and a spin coherent states and is valid in the limit h -> 0, j ->infinity with jh constant. The trace formula, obtained by taking the trace and the Fourier transform of the coherent state propagator, is compared to others found in the literature. (c) 2007 American Institute of Physics.481