We present a canonical account of the Berezin integral and associated Berezin expectation over Hilbert spaces of arbitrary dimension. Our account is illustrated by an extensive discussion of Gaussians, by a Berezinian version of the kernel theorem for generalized functions, and by an extension of the Shale–Stinespring theorem on spin transformations.
Cite this article
Paul Lee Robinson, The Berezin Calculus. Publ. Res. Inst. Math. Sci. 35 (1999), no. 2, pp. 123–194DOI 10.2977/PRIMS/1195143948