Supersymmetric models

Abstract

Supersymmetry in high-energy physics predicts bosonic and fermionic states with equal energies. Certain general ideas of supersymmetry were adopted to models in solid-state physics. They are often described by pairs of operators Q and Q †, which allow for pairs of Hamiltonians Q † Q and QQ† with the same spectrum. An example is the hydrogen atom. A class of models has the property Q 2 = 0. They yield either chiral models with pairs of energy levels E and − E if the Hamiltonian is linear in Q and Q †, or models with pairs of states with the same energy if the Hamiltonian is bilinear in Qand Q †.