Supersymmetry in the Pauli and Dirac Equation
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The first examples of supersymmetric quantum systems we have mentioned in Sect. 2.1.1 are the Pauli and Dirac Hamiltonian. Here we will discuss some of the implications of supersymmetry for systems which are characterized by these Hamiltonians. In particular, we will consider the Pauli paramagnetism of a two-and three- dimensional non-interacting electron gas. The (IDOS regularized) Witten index is shown to be related to the zero-temperature magnetization of such systems. It is also shown that breaking of SUSY gives rise to counterexamples of the so-called paramagnetic conjecture.
KeywordsDirac Equation Fermi Energy Constant Magnetic Field Witten Index Paramagnetic Susceptibility
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