Supersymmetry and Supersymmetric Quantum Mechanics
In this chapter we describe briefly, for the sake of completeness, some of the ideas and applications of supersymmetry, as defined and understood in other fields of physics. Supersymmetry was originally introduced in particle physics, more accurately, in relativistic quantum field theory where it was introduced in an attempt to obtain a unified description of the full range of fundamental interactions in nature.
As discussed in previous chapters, supersymmetry generates transformations between bosons and fermions. For normal symmetries the corresponding algebra involves only commutators, while supersymmetric algebras also include anti-commutators. The elements of a superalgebra can be interpreted as infinitesimal generators of a (super)symmetry, similar to the usual Lie algebra generators. In the simplest situation the supersymmetry generators commute with the hamiltonian, implying that boson and fermion states should be degenerate in energy.
In quantum field theory the degrees of...