ON THE FEYNMAN PATH CENTROID DENSITY AS A PHASE-SPACE DISTRIBUTION INQUANTUM-STATISTICAL MECHANICS

The phase space formulation of quantum statistical mechanics using the Feynman path centroid density offers an alternative perspective to th e standard Wigner prescription for the classical-like evaluation of eq uilibrium and/or dynamical quantities of statistical systems. The use of this formulation has been implicit in recent work on quantum rate t heories, for example, in which the centroid density distribution repla ces the classical Boltzmann distribution. In order to further understa nd the approximations involved in this and similar transcriptions, the present work elaborates and clarifies the issue of operator ordering in a rigorous centroid-based formulation. In particular, through the u se of the Weyl correspondence, a precise definition of the centroid sy mbol of operators and their products is presented. Though we fall shor t of finding the algebraic structure tantamount to that found in the W eyl symbols-of which the Wigner distribution is an example-the resulti ng expressions have internal consistency and are amenable to approxima te evaluation through cumulant expansions. (C) 1995 American Institute of Physics.