Invitation to unbounded representations of *- algebras on hilbert space
Schmüdgen, Konrad
Invitation to unbounded representations of *- algebras on hilbert space - Cham, Switzerland : Springer, 2020 - xviii, 381 p. : 9 illus. - Graduate texts in mathematics ; Volume 285. .
Includes bibliographical references and index.
This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers.
The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules.
Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
9783030463687
Associative rings and algebras
Hilbert algebras
Hilbert space
Lie groups
Operator algebras
Operator theory
Topological Groups, Lie Groups
Trace functionals
Unbounded representations
Quadratic modules
Infinitesimal representations
Weyl algebra
512.5 / SCH-I
Invitation to unbounded representations of *- algebras on hilbert space - Cham, Switzerland : Springer, 2020 - xviii, 381 p. : 9 illus. - Graduate texts in mathematics ; Volume 285. .
Includes bibliographical references and index.
This textbook provides an introduction to representations of general ∗-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers.
The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ∗-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ∗-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules.
Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference.
9783030463687
Associative rings and algebras
Hilbert algebras
Hilbert space
Lie groups
Operator algebras
Operator theory
Topological Groups, Lie Groups
Trace functionals
Unbounded representations
Quadratic modules
Infinitesimal representations
Weyl algebra
512.5 / SCH-I
