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Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics (North-Holland Mathematical Library)
Rok: 1987
ISBN: 9780444703217
OKCZID: 110074135
Citace (dle ČSN ISO 690):
JORGENSEN, Palle E. T. Operators and representation theory: canonical in quantum mechanics. Amsterodam: North-Holland, 1988, 337 s. ISBN 0-444-70321-7.
Hodnocení:
4.5 / 5
(6 hlasů)
Anotace
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.