Grassmann Variables, Supersymmetry and Supersymmetric ...
Grassmann Variables, Supersymmetry and Supersymmetric ...
Grassmann Variables, Supersymmetry and Supersymmetric ...
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Proof<br />
Fermionic Path Integral<br />
SUSY<br />
References<br />
The end<br />
<strong>Grassmann</strong> <strong>Variables</strong><br />
Path Integral<br />
N�<br />
� �<br />
dηi dηie i=1<br />
ηAη N�<br />
�<br />
=<br />
�<br />
dξi dξ ie<br />
i=1<br />
ξDξ N�<br />
�<br />
=<br />
�<br />
dξi<br />
�<br />
dξ i ie<br />
i=1<br />
λi ξi ξi =<br />
N�<br />
� �<br />
dξi<br />
�<br />
dξ i e<br />
i=1<br />
i<br />
λi<br />
N�<br />
�<br />
ξi ξi =<br />
�<br />
dξi<br />
�<br />
dξ i (1 + λiξ iξi) =<br />
i=1<br />
i<br />
N�<br />
�<br />
λi<br />
�<br />
dξi<br />
N�<br />
dξ i ξiξi = λi = detA<br />
i=1<br />
i=1<br />
Result �<br />
N�<br />
�<br />
i=1<br />
�<br />
dηi dηie ηAη = detA = e TrlnA<br />
Anna Pachol GV,SUSY ans SHO