A rigorous path integral for quantum spin using flat-space Wiener regularization

Adapting ideas of Daubechies and Klauder [J. Math. Phys. 26, 2239 (1985)] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrodinger semigroup on the Hilbert space L-2(R-2) of Lebesgue square-integrable functions on the Euclidean plane R-2. The path-integral formula emerges from the standard Feynman-Kac-Ito formula for the Schrodinger semigroup in the ultradiffusive limit of the underlying Brownian bridge on R-2. In a similar vein, a path-integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin Hamiltonian. (C) 1999 American Institute of Physics. [S0022-2488(99)02005-8].