Wiener measure for Heisenberg group
Heping Liu, Yingzhan Wang
TL;DR
This paper constructs Wiener measure on the Heisenberg group using the heat kernel of the sub-Laplacian, defines the Wiener integral, and establishes a Feynman-Kac formula for this setting.
Contribution
It introduces a Wiener measure for the Heisenberg group based on the sub-Laplacian heat kernel and formulates the Feynman-Kac formula in this non-commutative context.
Findings
Wiener measure constructed via heat kernel on Heisenberg group
Definition of Wiener integral in this setting
Feynman-Kac formula established for the Heisenberg group
Abstract
In this paper, we build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral. Then we give the Feynman-Kac formula.
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