PATH-INTEGRALS OF SPIN-J SYSTEMS IN THE HOLOMORPHIC REPRESENTATION

A path integral expression for the matrix element and the diagonal rep resentative of the spin-J evolution operator or Boltzmann factor is ob tained using Bloch coherent states in the holomorphic representation, yielding the appropriate boundary conditions. Quantum Dyson-Schwinger equations of motion are derived and used as criteria to select the app ropriate action. In the case of the diagonal representative the equati ons of motion satisfy the commutation relations of the spin operators and are the classical limit of the Dyson-Schwinger equations, if we re define the Lagrangian together with the integration measure. It is sho wn that in the case of a spin in a time-independent magnetic field the saddle-point approximation for both representatives gives the exact r esults. We present analytical algorithms to obtain the exponential fac tor and the prefactor in the saddle-point expansion, without an ad hoc reduction to an effective one-dimensional problem, but keeping instea d a 2 x 2 matrix structure. We apply our results to several models.