LATTICE APPROXIMATION OF QUANTUM-STATISTICAL TRACES AT A COMPLEX TEMPERATURE

We show that the addition of an imaginary part to the temperature in t he Gibbs ensemble will not destroy the convergence of the standard lat tice approximation scheme for quantum mechanical systems with Hamilton ians of the type (H) over cap = (p) over cap(2)/2m + V((x) over cap), provided the potential function V is real and bounded from below and i t satisfies the condition integral d(n)x exp(-tV(x)) < infinity for al l t > 0. As a by-product we obtain an explicit bound for the real-temp erature lattice kernels and a simple condition for the convergence of the real-temperature lattice expectation values of observables given b y polynomially bounded functions. (C) 1998 American Institute of Physi cs. [S0022-2488(98)00407-1].