Path Integrals and Coherent States of SU(2) and SU(1,1)

Path Integrals and Coherent States of SU(2) and SU(1,1)
Author: Akira Inomata
Publisher: World Scientific
Total Pages: 338
Release: 1992
Genre: Science
ISBN: 9789810206567

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.

Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference

Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference
Author: Valerio Tognetti
Publisher: World Scientific
Total Pages: 642
Release: 1999-04-01
Genre:
ISBN: 9814543845

This book contains the invited contributions to the 6th International Conference on Path Integrals from peV to TeV, held in Florence in 1998. The conference, devoted to functional integration, brought together many physicists with interests ranging from elementary particles to nuclear, solid state, liquid state, polymer and complex systems physics. The variety of topics is reflected in the book, which is a unique collection of papers on manifold applications of functional methods in several areas of physics.

Journal of Physics A

Journal of Physics A
Author:
Publisher:
Total Pages: 684
Release: 1998
Genre: Mathematical physics
ISBN:

Focuses on fundamental mathematical and computational methods underpinning physics. Relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics, classical and quantum integrable systems and classical and quantum field theory.

Functional Integration

Functional Integration
Author: Cécile Dewitt-Morette
Publisher: Springer
Total Pages: 450
Release: 1997-09-30
Genre: Mathematics
ISBN:

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.