Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Dover Books on Physics) - Softcover

Jorgensen, Palle E.T.; Physics

Softcover

ISBN 10: 0486466655 ISBN 13: 9780486466651

Publisher: Dover Publications, 2008

Synopsis

Algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This book begins with extensive background material that covers definitions and terminology, operators in Hilbert space, and the imprimitivity theorem.
Advancing to considerations of the algebras of operators in Hilbert space, the heart of the text examines domains of representations, operators in the enveloping algebra, and spectral theory. The final section explores covariant representations and connections, with a particular focus on infinite-dimensional Lie algebras. A helpful Appendix on the integrability of Lie algebras concludes the text.

About this title

From the Back Cover

Suitable for advanced undergraduates and graduate students in mathematics and physics, this three-part treatment of operators and representation theory begins with background material on definitions and terminology as well as on operators in Hilbert space. The introductory section concludes with a look at the imprimitivity theorem, which grounds in more mathematical language the work of Wigner on representations of the Poincaré and Galilei groups.
The second part of the monograph addresses the algebras of operators in Hilbert space, broadening the mathematics used in earlier versions of quantum theory. There are many examples in which the Hamiltonian, the operator that translates a quantum system in time, can be written as a polynomial in elements of an underlying Lie algebra. This section deals with properties of such operators. Part 3 explores covariant representation and connections, with a particular focus on infinite-dimensional Lie algebras. Connections to mathematical physics are stressed throughout the text, which concludes with three helpful appendixes, including a Guide to the Literature.
Dover (2017) revised and updated publication of the edition originally published by North-Holland Publishing Company, Amsterdam and New York, 1988.
www.doverpublications.com

About the Author

Palle E. T. Jorgensen is Professor of Mathematics at the University of Iowa.

Edition details

• Publisher: Dover Publications
• Publication date: 2008
• ISBN 10: 0486466655
• ISBN 13: 9780486466651
• Binding: Paperback
• Language: English
• Edition number: 2
• Number of pages: 352