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Title: Analytical mechanics for relativity and quantum mechanics ([Ebook]) / Oliver Davis Johns. Dewey Class: 531.01515 (DDC 22) Author: Johns, Oliver Davis. Publication: Oxford : Oxford University Press, 2010 Other name(s): Oxford Scholarship Online Physical Details: 1 online resource Series: Oxford graduate texts ISBN: 9780191717987 Note: Print publication date: 2005. - Published to Oxford Scholarship Online: January 2010 Mode of acces to digital resource: Digital reproduction.Oxford :Oxford University Press,2010. -Oxford Scholarship OnlineMode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher) System details note: Online access to this digital book is restricted to subscribing institutions through IP address (only for SISSA internal users) Summary Note: This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum mechanics. Comparisons to quantum mechanics appear throughout the text. The extended Hamiltonian theory with time as a coordinate is compared to Dirac’s formalism of primary phase space constraints. The chapter on relativistic mechanics shows how to use covariant Hamiltonian theory to write the Klein-Gordon and Dirac equations. The chapter on Hamilton-Jacobi theory includes a discussion of the closely related Bohm hidden variable model of quantum mechanics. Classical mechanics itself is presented with an emphasis on methods, such as linear vector operators and dyadics, that will familiarise the student with similar techniques in quantum theory. Several of the current fundamental problems in theoretical physics, such as the development of quantum information technology and the problem of quantising the gravitational field, require a rethinking of the quantum-classical connection.: ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
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