{"product_id":"9780387983189","title":"Mathematical Topics Between Classical and Quantum Mechanics","description":"This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":47013146919152,"sku":"9780387983189","price":219.99,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780387983189_p0.jpg?v=1763696196","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780387983189","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}