{"product_id":"introduction-to-nambus-generalized-hamiltonian-dynamics-9789819570294","title":"Introduction to Nambu's Generalized Hamiltonian Dynamics","description":"\u003cp\u003e • Author(s): Tamiaki Yoneya\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Physics - Mathematical \u0026amp; Computational\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book introduces Nambu's generalized Hamiltonian dynamics. In 1973, Nambu proposed extending classical Hamiltonian mechanics by replacing the canonical doublet (\u003cem\u003ep\u003c\/em\u003e, \u003cem\u003eq\u003c\/em\u003e) with a three-dimensional phase space defined by a canonical triplet (\u003cem\u003ex\u003c\/em\u003e, \u003cem\u003ey\u003c\/em\u003e, \u003cem\u003ez\u003c\/em\u003e). The equations of motion are formulated using a triple bracket--a generalization of the Poisson bracket--with two 'Hamiltonians' treated on an equal footing. This framework can further be extended to an \u003cem\u003en\u003c\/em\u003e-tuple of phase-space coordinates, an \u003cem\u003en\u003c\/em\u003e-bracket, and equations of motion involving \u003cem\u003en\u003c\/em\u003e-1 Hamiltonians in an \u003cem\u003en\u003c\/em\u003e-dimensional phase space. Nambu's original motivation was to generalize the Liouville theorem, which states that the volume of an ensemble in phase space is preserved under dynamical flows--a principle fundamental to statistical mechanics. He sought to construct systems with analogous properties for arbitrary-dimensional phase spaces, including odd dimensions. Although his proposal attracted little attention for more than a decade, subsequent developments revealed its relevance in diverse areas of theoretical and mathematical physics, notably in string\/M-theory and fluid mechanics. This book introduces the reader to classical Nambu dynamics by explaining its principal aspects from an elementary viewpoint and developing it further from a coherent and unified standpoint. It is intended for readers with a reasonable understanding of classical analytical mechanics and working knowledge of basic physics and standard mathematical methods in theoretical physics.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":47969471692951,"sku":"9789819570294","price":11180.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9789819570294.webp?v=1782921982","url":"https:\/\/atlanticbooks.com\/products\/introduction-to-nambus-generalized-hamiltonian-dynamics-9789819570294","provider":"Atlantic Books","version":"1.0","type":"link"}