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 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-u.s3.eu-west-1.amazonaws.com/9781351045551/4730f38a-3e35-40e9-9674-aa9748370ac3/content/eq1.tif"/>