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 the 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 traces, a distributional version of the natural extension, and a generalized 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 well as to the projective tenser product of Hilbert spaces from functional analysis.
Journal of Theoretical Probability
Betounes, D. E.
(1995). Trace Operators, Feynman Distributions, and Multiparameter White-Noise. Journal of Theoretical Probability, 8(1), 119-138.
Available at: https://aquila.usm.edu/fac_pubs/5951