Lie algebras, cohomology, and new applications to quantum mechanics, : AMS special session on lie algebras, cohomology, and new applications to quantum mechanics, March 20-21, 1992, Southern Missouri State University / Niky Kamran, Peter J. Olver, editors.

Format:

Book

Contributor:

Kamran, Niky, 1959- editor.

Olver, Peter J., editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 160

Contemporary mathematics, 160 0271-4132

Language:

English

Subjects (All):

Lie algebras.

Homology theory.

Quantum theory.

Physical Description:

1 online resource (viii, 310 p. ) ill. ;

Edition:

1st ed.

Place of Publication:

Providence, RI : American Mathematical Society, [1994]

Language Note:

English

Summary:

This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrödinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents a look at some of the current developments in this extraordinarily rich and vibrant area.

Contents:

Intro

Contents

Preface

Hidden symmetries of differential equations

Algebraic methods in scattering

Exact solutions to operator differential equations

The algebra of tensor operators for the unitary groups

Lie groups and probability

Coherent tensor operators

Uq(sl(2)) and q-special functions

The group representation matrix in quantum mechanical scattering

Quasi-exact solvability

Quantization and deformation of Lie algebras

Algebraic theory

The time-dependent Schrödinger equation in multidimensional integrable evolution equations

Models of q-algebra representations: Matrix elements of Uq(su2)

Many-electron correlation problem and Lie algebras

Quasi-exactly-solvable spectral problems and conformal field theory

Lie-algebras and linear operators with invariant subspaces.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-7751-8

0-8218-5494-1