Trace Operators, Feynman Distributions, and Multiparameter White-Noise
Document Type
Article
Publication Date
1-1-1995
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
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.
Publication Title
Journal of Theoretical Probability
Volume
8
Issue
1
First Page
119
Last Page
138
Recommended Citation
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