The Berezin Calculus

  • Paul Lee Robinson

    University of Florida, Gainesville, USA


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. 123–194

DOI 10.2977/PRIMS/1195143948