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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Symbol Correspondences for Spin Systems (Hardcover, 2014 ed.)
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Symbol Correspondences for Spin Systems (Hardcover, 2014 ed.)
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In mathematical physics, the correspondence between quantum and
classical mechanics is a central topic, which this book explores in
more detail in the particular context of spin systems, that is,
SU(2)-symmetric mechanical systems. A detailed presentation of
quantum spin-j systems, with emphasis on the SO(3)-invariant
decomposition of their operator algebras, is first followed by an
introduction to the Poisson algebra of the classical spin system
and then by a similarly detailed examination of its SO(3)-invariant
decomposition. The book next proceeds with a detailed and
systematic study of general quantum-classical symbol
correspondences for spin-j systems and their induced twisted
products of functions on the 2-sphere. This original systematic
presentation culminates with the study of twisted products in the
asymptotic limit of high spin numbers. In the context of spin
systems it shows how classical mechanics may or may not emerge as
an asymptotic limit of quantum mechanics. The book will be a
valuable guide for researchers in this field and its self-contained
approach also makes it a helpful resource for graduate students in
mathematics and physics.
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