The Berezin integral is differentiation with respect to a Grassmann variable: and . A finite-dimensional fermionic Gaussian integral gives a determinant or Pfaffian.
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The Berezin integral is a concept from mathematical physics, particularly in the field of supersymmetry and quantum mechanics. It is a type of integral used for integrating functions of Grassmann variables, which are anticommuting variables that the Berezin calculus is built around. Grassmann variables play a fundamental role in the formulation of supersymmetry, where they are used to describe fermionic fields or states.