Geometric study of the connection between the Lagrangian and Hamiltonian constraints |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Tromsø, 90-37 Tromsø, Norway;2. Department of Mathematics and Natural Sciences, University of Stavanger, 40-36 Stavanger, Norway;3. Faculty of Mathematics and Computer Science, University of Warmia and Mazury, ul. Słoneczna 54, 10-710 Olsztyn, Poland;1. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany;2. Instituto de Física Teórica, UAM-CSIC, Madrid, Spain;3. Fakultät für Physik, Technische Universität München, James-Franck-Str. 1, D-85748 Garching, Germany |
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| Abstract: | The second order differential equation character of the solutions of the dynamical equation i(Γ)ωL = dEL for a singular Lagrangian L, as well as the conditions for the existence of such a solution, are studied. We also introduce a couple of maps R (L)v : T FL(v)(T1Q) → Tv(TQ) and T(L)v : TFL(v)(T1Q) → TFL(v)(T1Q), with v ϵ TQ, which are shown to be very useful for establishing the connection between the constraints arising in the Lagrangian and Hamiltonian formulations. |
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