Fock Space, the Heisenberg Group, Heat Flow, and Toeplitz Operators

I discuss some work which has given significant insight into the analytic structure of a space first studied in the late 1920’s by the distinguished Soviet physicist Vladimir A. Fock [16]. Here, C ⁿ is complex n-space and, for z in C ⁿ , we consider the standard family of Gaussian measures https://www.w3.org/1998/Math/MathML"> d μ t ( z ) = ( 4 π t ) − n exp ( − | z | 2 / 4 t ) d v ( z ) , t > 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781351045551/0d0c2edd-5761-460a-bbe7-0d763d2f484f/content/eq1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>