Supersymmetric Methods in Quantum and Statistical Physics

Supersymmetry is a very important topic in high energy physics, from both theoretical and phenomenological points of view. What is less well-known is the fact that supersymmetry is also a very powerful mathematical idea in quantum mechanics and statistical physics. Supersymmetric Methods in Quantum and Statistical Physics by Georg Junker gives an introduction to supersymmetric quantum mechanics and supersymmetric methods in statistical physics.

The book assumes some familiarity with quantum mechanics, though no knowledge of quantum field theory or supersymmetry is assumed.

The main topics are the Witten model, supersymmetric classical mechanics, shape-invariant potentials and exact solutions, supersymmetry in classical stocastic dynamics and supersymmetry in the Pauli & Dirac equations. Once supersymmetric mechanics was seen as a “test model” for theoretical high energy physics, but the ideas have now reached wider interest in physics.

Chapter 1 starts with a general introduction to supersymmetry. This chapter exposes the reader to basic ideas of supersymmetry in field theory and introduces supersymmetric quantum mechanics.

Supersymmetric quantum mechanics is the topic of Chapter 2. Here one is introduced to supersymmetry in quantum mechanics rather generally and then Witten’s N=2 supersymmetric model which is the main focus of most approaches to supersymmetric quantum mechanics.

In Chaper 3 the Witten model is discussed in further detail. Topics here include: Witten parity, the SUSY potential, zero-energy states & good SUSY and the asymptotic behaviour of the SUSY potential. Examples are included.

In Chapter 4 supersymmetric classical mechanics is reviewed. Topics here include: pseudoclassical mechanics, supersymmetric classical mechanics, the classical dynamics and quantisation via the canonical approach and path-integrals.

Exact solutions of the eigenvalue problem is the subject of Chapter 5. Here the reader is introduced to shape-invariant potentials and exact solutions. Examples and a comparison to the factorisation method are presented.

Chapter 6 discusses path-integration in further detail. Topics include: the WKB approximation, quasi-classical quantisation conditions and quasi-clasical eigenfunctions. Exactly solvable examples are presented as well as some numerical investigations.

Supersymmetry in classical stochastic dynamics is the subject of Chapter 7. Topics include: supersymmetry in the Fokker-Planck & Lengevin equations and the implications of good/broken supersymmetry.

Chapter 8 discusses supersymmetry in the Pauli & Dirac equations.

The final chapter, Chapter 8 gives concluding remarks and an overview. Here a list of textbooks covering supersymmetry in high energy physics is give. A table of applications of supersymmetry in theoretical physics is also included.

A rather large set of references is given.

Hardcover: 172 pages
Publisher: Springer (September 30, 1996)
Language: English
ISBN-10: 3540615911
ISBN-13: 978-3540615910