Grassmann Variables, Supersymmetry and Supersymmetric ...

Partition function
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Z =
Fermionic Path Integral
SUSY
References
The end
Grassmann Variables
Path Integral
DψDψe i � d 4 xψ(iγ µ ∂µ−m)ψ = C det(iγ µ ∂µ−m) = C e Trln(iγµ ∂µ−m)
G (2) (x1, x2) =
Two point Green function:
� DψDψe i � d 4 xψ(iγ µ ∂µ−m)ψ ψ(x1)ψ(x2)
� DψDψe i � d 4 xψ(iγ µ ∂µ−m)ψ
= C det(iγµ ∂µ − m)[−i(iγ µ ∂µ − m)] −1
C det(iγ µ ∂µ − m)
⇒ (in Fourier space):
G (2) �
(x1, x2) = S(x1 − x2) =
Anna Pachol GV,SUSY ans SHO
⇒
d 4p (2π) 4
ie−ip(x1−x2) p − m + iɛ
=