Gaussian Integrals Over Grassmann Variables
The following formulas for Gaussian integrals are used often in the path integral formulation of quantum field theory:
with being a matrix.
with being an antisymmetric matrix. In the above formulas the notation is used.
From the above formulas, other useful formulas follow:
with being an invertible matrix, and are Grassmann variables.
with being an invertible antisymmetric matrix, and Grassmann variable.
Read more about this topic: Grassmann Integral
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