Grassmann Variables, Supersymmetry and Supersymmetric ...

Dirac field
Fermionic Path Integral
SUSY
References
The end
Grassmann Variables
Path Integral
In similar way we can prove:
� dη � dη ηiηje ηAη = (detA)(A −1 )ji
A Grassmann field is a function of spacetime whose values are
anticommuting numbers. We can define a Grassmann field ψ(x) in
terms of any set of orthonormal basis functions:
ψ(x) = �
ψiφi(x)
The basis functions φi(x) are ordinary complex valued functions,
while the coefficients ψi are Grassmann numbers.
To describe the Dirac field we take the φi to be a basis of
four-component spinors.
i
Anna Pachol GV,SUSY ans SHO