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The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.
The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy.
The final chapters present the theory of the SU(1, 1) coherent states and their applications. The radial coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included.This book will be useful as an introduction to the subject as well as a valuable work of reference.
Contents:
- Part I Path Integrals for SU(2) and SU(1,1) (A Inomata):
- Introduction
- Techniques for Path Integration
- Path Integrals on SU(2)
- Path Integrals for SU(1,1)
- Exactly Path-Integrable Examples
- Part II Path Integrals in the SU(2) Coherent State Representation and Related Topics (H Kuratsuji):
- Introduction
- Glauber States Revisited
- SU(2) Coherent States and Their Generalization
- Path Integrals for Spin and Unitary Spin
- Semiclassical Quantization Theory
- Applications
- Nonlinear Field Model
- Phase Holonomy
- Part III SU(1,1) Coherent States and Path Integrals for SU(1,1) (C C Gerry):
- Introduction
- SU(1,1) and the Perelemov Coherent States
- Path Integral and Classical Dynamics
- Applications in Quantum Mechanics
- Application to Quantum Optics
Readership: Physicists.
