An Invitation to Unbounded Representations of -Algebras on Hilbert Space

This textbook provides an introduction to representations of general $\ast$-algebras by unbounded operators on Hilbert space, covering both the general theory and representations of special classes. It is aimed at graduate students and researchers in advanced functional analysis and mathematical physics, with many exercises and a valuable reference list.

Format: Paperback / softback
Length: 381 pages
Publication date: 29 July 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers an in-depth exploration into the representation of general $\mathbb{*}$-algebras by unbounded operators on Hilbert space, a subject that naturally arises in quantum mechanics but has primarily been addressed in advanced monographs tailored for researchers. Spanning both the general theory of unbounded representation theory on Hilbert space and the representation of significant special classes of $\mathbb{*}$-algebras, such as the Weyl algebra and enveloping algebras associated with unitary representations of Lie groups, the book delves into a wide range of topics that have previously been treated in a fragmented manner. These topics encompass group graded $\mathbb{*}$-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations, and representations on rigged modules. By presenting advanced material in a readily accessible format, this book caters to graduate students and scholars seeking to delve into advanced functional analysis and mathematical physics. With numerous exercises included, it serves as an invaluable resource for courses focusing on the representation theory of Lie groups and their applications to quantum physics. Additionally, the book features a comprehensive selection of material and bibliographic notes, making it a valuable reference for researchers and scholars in the field.

Weight: 611g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030463687
Edition number: 1st ed. 2020