Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (Dover Books on Physics) - Softcover
Synopsis
The algebras of operators arise frequently in the study of representations of Lie groups, both finite-dimensional and infinite-dimensional. This survey begins with extensive background material and advances to considerations of the algebras of operators in Hilbert space and covariant representations and connections. 1988 edition.
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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 Poincare 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.
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Operators and Representation Theory (Paperback)
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Dover Publications Inc., New York, 2008
ISBN 10: 0486466655
ISBN 13: 9780486466651
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Paperback. Condition: new. Paperback. 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. This survey of operators in Hilbert space offers extensive background material and covers domains of representation, operators in the enveloping algebra, spectral theory, covariant representation, and infinite-dimensional Lie algebras. 1988 edition. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780486466651
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Operators and Representation Theory
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Operators and Representation Theory
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