Grassmann Variables, Supersymmetry and Supersymmetric ...
Grassmann Variables, Supersymmetry and Supersymmetric ...
Grassmann Variables, Supersymmetry and Supersymmetric ...
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Fermionic Path Integral<br />
SUSY<br />
References<br />
The end<br />
Complex <strong>Grassmann</strong> variables<br />
<strong>Grassmann</strong> <strong>Variables</strong><br />
Path Integral<br />
Since Dirac field is complex-valued, we have to introduce complex<br />
<strong>Grassmann</strong> numbers: η, θ <strong>and</strong> define the complex conjugation to<br />
reverse the order of products: (θη) ≡ ηθ = −θη<br />
To integrate over complex <strong>Grassmann</strong> numbers, let us define:<br />
η = η1 + iη2<br />
√ 2<br />
<strong>and</strong> η = η1 − iη2<br />
√ 2<br />
now we can treat η; η as independent <strong>Grassmann</strong> numbers <strong>and</strong><br />
adopt the convention � dη � dηηη = 1<br />
Anna Pachol GV,SUSY ans SHO
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