Grassmann Variables, Supersymmetry and Supersymmetric ...

Fermionic Path Integral
SUSY
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Supersymmetric harmonic oscillator
Supersymmetry
Supersymmetric harmonic oscillator
1. Harmonic bosonic oscillator.
Hamiltonian:HB = 1
2p2 + 1
2ω2 Bq2 where p and q are the
momentum and coordinate operators respectively and [p, q] = 1
Hamiltonian can be presented in terms of bosonic
creation-annihilation operators: b † , b, as follows:
HB = 1
2 ωB{b † , b} = 1
2 ωB(b † b + bb † )
where � = 1; m = 1; b = 1
√ 2ωB (ip + ωBq) and
[b, b † ] = 1; [b, b] = 0; [b † , b † ] = 0; [NB, b] = −b; [NB, b † ] = b †
and NB = b † b is bosonic number operator.
Anna Pachol GV,SUSY ans SHO