{"product_id":"cqmechanics-a-unification-of-quantum-classical-mechanics-quantum-semi-classical-entanglement-quantum-classical-path-integrals-9780997076189","title":"CQMechanics: A Unification of Quantum \u0026 Classical Mechanics: Quantum\/Semi-Classical Entanglement, Quantum\/Classical Path Integrals,","description":"\u003cp\u003e • Author(s): Stephen Blaha\u003cbr\u003e • Publisher: Pingree-Hill Publishing\u003cbr\u003e • Publisher Imprint: Pingree-Hill Publishing\u003cbr\u003e • BISAC: Physics - Mathematical \u0026amp; Computational\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe relation of quantum and classical phenomena has been a subject of continuing interest. Most studies approximate the quantum description of a phenomenon to obtain a classical or semi-classical approximation. This book develops a new formalism that contains both fully quantum and classical sectors, and a continuous transformation between them that provides an intermediate partly quantum - partly classical sector. This intermediate sector can play the role of a bridge between the quantum and classical descriptions of a process. Using this new formalism we consider the case of the harmonic oscillator in detail relating the quantum oscillator through the bridge to the classical oscillator. We then develop a generalization of the Feynman path integral formalism that has both a normal quantum sector and also a 'new' classical path integral sector - again with a partly quantum-partly classical intermediate sector. Our path integral generalization yields a generalization of the Schroedinger equation with both quantum and classical 'wave function' solutions. We also apply this formalism to the Fokker-Planck equation, for which it is naturally adapted. Next we apply the new formalism to quantum field theories that are known to be chaotic, and then generate a classical sector - also with chaotic behavior. We also take the standard approach to quantum entanglement and show how to extract a semi-classical entanglement as well as a classical limit without entanglement. The Boltzmann equation is easily placed within the framework of our new formalism. We solve a special case of the Vlasov equation as an example. A special relativistic Boltzmann equation is also developed within the framework of our formalism. Lastly, we develop our formalism for boson and fermion quantum field theory. We give a sensible reason why Nature must be quantum.\u003c\/p\u003e","brand":"Atlantic Books","offers":[{"title":"Hardcover","offer_id":46494488428695,"sku":"9780997076189","price":2728.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780997076189.webp?v=1769174630","url":"https:\/\/atlanticbooks.com\/products\/cqmechanics-a-unification-of-quantum-classical-mechanics-quantum-semi-classical-entanglement-quantum-classical-path-integrals-9780997076189","provider":"Atlantic Books","version":"1.0","type":"link"}