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An Invitation to Unbounded Representations of -Algebras on Hilbert Space (Paperback, 1st ed. 2020)
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An Invitation to Unbounded Representations of -Algebras on Hilbert Space (Paperback, 1st ed. 2020)
Series: Graduate Texts in Mathematics, 285
Expected to ship within 10 - 15 working days
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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 Positivstellensatze, 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.
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