Finite-temperature and supercharged ideal supersymmetric matter

We investigate the properties of simple, ideal supersymmetric matter in 0+1 and 3+1 dimensions at finite temperature and finite supercharge density. The functional dependence of the partition function Z on the temperature T and chemical potential μ is qualitatively different from the usual situation of a net U(1) charge density, such as electric charge or fermion number. This is a consequence of the fact that the Hamiltonian H is the square of the supercharge Q, H = Q2