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Supersymmetry In Quantum and Classical Mechanics

By Bijan Kumar Bagchi

Series Editor: Alan Jeffrey, Haim Brezis, Ronald G. Douglas

Published September 21st 2000 by Chapman and Hall/CRC – 240 pages

Series: Monographs and Surveys in Pure and Applied Mathematics

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Description

Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years, progress in this field has been dramatic and the literature continues to grow. Until now, no book has offered an overview of the subject with enough detail to allow readers to become rapidly familiar with its key ideas and methods.

Supersymmetry in Classical and Quantum Mechanics offers that overview and summarizes the major developments of the last 15 years. It provides both an up-to-date review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.

Reviews

"This interesting and instructive monograph partially fills the gap in the literature concerning the subject of quantization of supersymmetric systems in general. It gives a brief account of many major developments of non-relativistic supersymmetric quantum mechanics (SSQM) in the last fifteen years."

- Mathematical Reviews, November 2001

Contents

GENERAL REMARKS ON SUPERSYMMETRY

Background

BASIC PRINCIPLES OF SUPERSYMMETRIC QUANTUM MECHANICS

SUSY and the Oscillator Problem

Superpotential and Setting Up a Supersymmetric Hamiltonian

Physical Interpretation of Hs

Properties of the Partner Hamiltonians

Applications

Superspace Formalism

Other Schemes of SUSY

SUPERSYMMETRIC CLASSICAL MECHANICS

Classical Poisson Bracket, Its Generalizations

Some Algebraic Properties of the Generalized Poisson Bracket

A Classical Supersymmetric Model

SUSY Breaking, Witten Index and Index Condition

SUSY Breaking

Witten Index

Finite Temperature SUSY

Regulated Witten Index

Index Condition

q-Deformation and Index Condition

Parabosons

Deformed Parabose States and Index Condition

Witten's Index and Higher-Derivative SUSY

Explicit SUSY Breaking and Singular Superpotentials

FACTORIZATION METHOD, SHAPE INVARIANCE AND GENERATION OF SOLVABLE PROBLEMS

Preliminary Remarks

Factorization Method of Infeld and Hull

Shape Invariance Condition

Self-Similar Potentials

A Note on the Generalized Quantum Condition

Non-Uniqueness of the Factorizability

Phase Equivalent Potentials

Generation of Exactly Solvable Potentials in SUSYQM

Conditionally Solvable Potentials and SUSY

RADIAL PROBLEMS AND SPIN-ORBIT COUPLING

SUSY and the Radial Problems

Radial Problems Using Ladder Operator Techniques in SUSYQM

Isotropic Oscillator and Spin-Orbit Coupling

SUSY in D- Dimensions

SUPERSYMMETRY IN NONLINEAR SYSTEMS

The KdV Equation

Conservation Laws in Nonlinear Systems

Lax Equations

SUSY and Conservation Laws in the KdV - MKdV Systems

Darboux's Method

SUSY and Conservation Laws in the KdV-SG Systems

Supersymmetric KdV

Conclusion

PARASUPERSYMMETRY

Introduction

Models of PSUSYQM

PSUSY of Arbitrary Order p

Truncated Oscillator and PSUSYQM

Multidimensional Parasuperalgebras

APPENDIX

Note: Each chapter also contains a References section

Name: Supersymmetry In Quantum and Classical Mechanics (Hardback) – Chapman and Hall/CRC 
Description: By Bijan Kumar BagchiSeries Editor: Alan Jeffrey, Haim Brezis, Ronald G. Douglas. Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent...
Categories: Quantum Mechanics, Differential Equations, Mathematical Physics