ENGLISH

Operators and representation theory: canonical models for algebras of operators arising in quantum mechanics

By Palle E.T. Jorgensen (Eds.)

Book information

Publisher
North-Holland
Year
1988
ISBN
0444703217, 9780444703217, 9780080872582
LCC
QA1 .N86 no. 120,QA326 .N86 no. 120
Language
english
Format
DJVU
Filesize
2 MB (1807703 bytes)
Series
Notas de matematica 120 North-Holland mathematics studies 147
Pages
ii-vi, 1-337\345
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

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.

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