Supersymmetric Methods in Quantum and Statistical Physics

This book gives an introduction to supersymmetric quantum mechanics and a comprehensive review of its applications in quantum and statistical physics. The classical version and the quantum version of Witten's model are studied in detail. Exact spectral properties of the model for the so-called shape invariant potentials are discussed. The quasi-classical quantization rules are derived. The topics covered also include the supersymmetric structure of a classical stochastic dynamical system obeying the Langevin or the Fokker-Planck equation, Pauli's Hamiltonian and its application to the paragmagnetism of a non-interacting electron gas in two and three dimensions, supersymmetry of Dirac's Hamiltonian, and others. The book addresses graduate students as well as scientists.
TOC: Contents: Introduction.- Supersymmetric Quantum Mechanics.- The Witten Model.- Supersymmetric Classical Mechanics.- Exact Solution of Quantum-Mechanical Eigenvalue Problems.- Quasi-Classical Path-Integral Approach.- Supersymmetry in Classical Stochastic Dynamics.- Supersymmetry in the Pauli and Dirac Equations.- Concluding Remarks.- References.- Author Index.- Subject Index.