P. E. T. Jorgensen

Operators and Representation Theory (eBook, PDF)

Canonical Models for Algebras of Operators Arising in Quantum Mechanics

• Format: PDF

Produktbeschreibung

Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.

This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C^*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra.

Also examined are C^*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem.

Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers.

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Produktdetails

• Verlag: Elsevier Science & Techn.
• Seitenzahl: 336
• Erscheinungstermin: 1. Dezember 1987
• Englisch
• ISBN-13: 9780080872582
• Artikelnr.: 38124975