Trace formula for systems with spin from the coherent state propagator

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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 \hbar -> 0, j -> \infty with j\hbar 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.