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. Thebook
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.
