TRACE OPERATORS, FEYNMAN DISTRIBUTIONS, AND MULTIPARAMETER WHITE-NOISE

Within the framework of white noise analysis on the probability space Omega = L(R(d), R(M)), the recent work by Johnson and Kallianpur on t he Hu-Meyer formula, traces, and natural extensions is generalized to the multiparameter case: d>1. Besides providing a more general setting for these topics, the paper gives an alternative definition for the t races, a distributional version of the natural extension, and a genera lized Kallianpur-Feynman distribution. The development illustrates how traces and natural extensions are intimately related to Wick products and the change of covariance formula from quantum field theory, as we ll as to the projective tenser product of Hilbert spaces from function al analysis.