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 />
Basic idea of <strong>Supersymmetry</strong><br />
<strong>Supersymmetry</strong><br />
<strong>Supersymmetric</strong> harmonic oscillator<br />
Hilbert space contain Fermionic <strong>and</strong> Bosonic Hilbert spaces:<br />
H = HB ⊕ HF<br />
Coordinates space : (xµ, θµ) <strong>and</strong> Momentum space : (pα, ηα)<br />
where xµ <strong>and</strong> pα are bosonic variables i.e. commuting :<br />
[xµ, xν] = 0; [pα, pβ] = 0<br />
<strong>and</strong> θµ, ηα are fermionic variables i.e. anticommuting (grassmanian<br />
numbers) : {θµ, θν} = 0; {ηµ, ην} = 0<br />
A supersymmetry transformation turns a bosonic state into a<br />
fermionic state, <strong>and</strong> vice versa. The operator Q that generates<br />
such transformations must be an anticommuting spinor, with<br />
Q|Boson >= |Fermion >, Q † |Fermion >= |Boson ><br />
Anna Pachol GV,SUSY ans SHO
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