{"product_id":"9780997076189","title":"CQMechanics: A Unification of Quantum \u0026 Classical Mechanics: Quantum\/Semi-Classical Entanglement, Quantum\/Classical Path Integrals, Quantum\/Classical Chaos","description":"\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\u003cp\u003e\u003c\/p\u003e","brand":"Pingree-Hill Publishing","offers":[{"title":"Default Title","offer_id":49779009945840,"sku":"9780997076189","price":29.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9780997076189_p0.jpg?v=1780094826","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9780997076189","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}