Berezin integral

In mathematical physics, a Berezin integral, named after Felix Berezin, (or Grassmann integral, after Hermann Grassmann) is a way to define integration of elements of the exterior algebra (Hermann Grassmann 1844). It is called integral because it is used in physics as a sum over histories for fermions, an extension of the path integral.

Let ${\displaystyle \Lambda ^{n}}$ be the exterior algebra of polynomials in anticommuting elements ${\displaystyle \theta _{1},\dots ,\theta _{n}}$ over the field of complex numbers. (The ordering of the generators ${\displaystyle \theta _{1},\dots ,\theta _{n}}$ is fixed and defines the orientation of the exterior algebra.) The Berezin integral on ${\displaystyle \Lambda ^{n}}$ is the linear functional ${\displaystyle \int _{\Lambda ^{n}}\cdot {\textrm {d}}\theta }$ with the following properties:

...
Wikipedia