On the path integral representation for spin systems

We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second-class constraints the Dirac brackets of the proposed theory represent the commutation relations for the spin. We show that the corresponding partition function, obtained via the Fadeev-Senjanovic procedure, coincides with that obtained using coherent states. We also evaluate this partition function for the case of a single spin in a magnetic field.