Grassmann Variables, Supersymmetry and Supersymmetric ...

Fermionic Path Integral
SUSY
References
The end
Basic idea of Supersymmetry
Supersymmetry
Supersymmetric harmonic oscillator
The generators Q and Q † must satisfy an algebra of
anticommutation and commutation relations with the schematic
form:
{Q, Q † } = Pµ, {Q, Q} = {Q † , Q † } = 0, [Pµ, Q] = [Pµ, Q † ] = 0,
where Pµ is the four-momentum generator of spacetime
translations.
The single-particle states of a supersymmetric theory fall into
irreducible representations of the supersymmetry algebra, called
supermultiplets.
Each supermultiplet contains both fermion and boson states,
which are commonly known as superpartners of each other.
By definition, if |Ω > and |Ω ′ > are members of the same supermultiplet,
then |Ω ′ > is proportional to some combination of Q and Q † operators acting
on |Ω >, up to a spacetime translation or rotation.
Anna Pachol GV,SUSY ans SHO