Download e-book for iPad: Geometry from Dynamics, Classical and Quantum by José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe

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By José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi

This publication describes, by utilizing ordinary options, how a few geometrical constructions established this present day in lots of components of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. it's assumed that what should be accessed in real stories while learning a given approach is simply its dynamical behavior that is defined through the use of a relations of variables ("observables" of the system). The publication departs from the main that ''dynamics is first'' after which attempts to reply to in what experience the only real dynamics determines the geometrical constructions that experience proved so precious to explain the dynamics in such a lot of vital circumstances. during this vein it truly is proven that almost all of the geometrical constructions which are utilized in the traditional shows of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are decided, although regularly now not uniquely, through the dynamics on my own. an identical software is comprehensive for the geometrical constructions appropriate to explain quantum dynamics. ultimately, it really is proven that extra homes that permit the specific description of the dynamics of sure dynamical platforms, like integrability and large integrability, are deeply regarding the former improvement and should be covered in the last a part of the booklet. The mathematical framework used to offer the former application is stored to an ordinary level throughout the textual content, indicating the place extra complicated notions can be had to continue additional. A family members of proper examples is mentioned at size and the mandatory rules from geometry are elaborated alongside the textual content. besides the fact that no attempt is made to give an ''all-inclusive'' creation to differential geometry as many different books exist already out there doing precisely that. However, the advance of the former software, regarded as the posing and answer of a generalized inverse challenge for geometry, results in new methods of considering and pertaining to one of the most conspicuous geometrical buildings showing in Mathematical and Theoretical Physics.

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Geometry from Dynamics, Classical and Quantum by José F. Cariñena,Alberto Ibort,Giuseppe Marmo,Giuseppe Morandi

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