The spin coherent state path integral describing the dynamics of a spin-12system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exac...

We study the quantum Knizhnik-Zamolodchikov equation of level 0 associated with the spin 1/2 representation of Uq(ŝl2). We find an integral formula for solutions in the case of an arbitrary total spin and |q| < 1. In the formula, different solutions can be obtained by taking different integral kernels with the cycle of integration being fixed. ⋆ A Fellow of the Japan Society for the Promotion o...

Polyakov’s spin factor enters as a weight in the path-integral description of particlelike modes propagating in Euclidean space-times, accounting for particle spin. The Fock-Feynman-Schwinger path integral applied to QCD accomodates Polyakov’s spin factor in a natural manner while, at the same time, it identifies Wilson line (loop) operators as sole agents of interaction dynamics among matter a...

The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index–spinor formulation within the BFV–BRST approach. None renor-malizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index–free form with the use of index spinor. The choice of boundary conditions on the i...

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the...

Nonlinear longitudinal relaxation of a spin in a uniform external dc magnetic field is treated using a master equation for the quasiprobability distribution function of spin orientations in the configuration space of polar and azimuthal angles (analogous to the Wigner phase space distribution for translational motion). The solution of the corresponding classical problem of the rotational Browni...

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 Schrödinger semigroup on the Hilbert space L2(R2) of Lebesgue square-int...

Integral equations for the spin-weighted spheroidal wave functions is given . For the prolate spheroidal wave function with m = 0, there exists the integral equation whose kernel is sin x x , and the sinc function kernel sin x x is of great mathematical significance. In the paper, we also extend the similar sinc function kernel sin x x to the case m 6= 0 and s 6= 0, which interestingly turn out...

Within a wide class of ferromagnetic and antiferromagnetic systems, quantum tunneling of magnetization direction is spin-parity dependent: it vanishes for magnetic particles with half-integer spin, but is allowed for integer spin. A coherent-state path integral calculation shows that this topological effect results from interference between tunneling paths.

The spin-statistics connection is derived in a simple manner under the postulate that the original and the exchange state vectors are only superposed with the plus sign. The single-particle state vectors must however exhibit dependence on the angle χ of rotations in spin space about the spin-quantization axis. This means that not only a spin-quantization axis but a complete quantization frame m...