Hamiltonian Structures in the Quantum Theory of Hamilton–Dirac Systems - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Доклады Академии Наук / Doklady Mathematics Année : 2015

Hamiltonian Structures in the Quantum Theory of Hamilton–Dirac Systems

Résumé

This paper discusses the Hamiltonian aspects of the quantum theory of constrained Hamiltonian systems; in particular, we extend results of [9, 6] to such systems. In this paper, we usually refer to these systems as Hamilton–Dirac systems, because it was Dirac who first defined them (under the name of generalized Hamiltonian systems). Such systems arise in the application of the Legendre transform to unconstrained Lagrangian systems with singular Lagrange function (for which the Legendre transform is noninvertible). It should be emphasized that constrained Hamiltonian systems bear no relation to Lagrangian systems with holonomic constraints; however, them can be regarded as objects dual to Lagrangian systems with nonholonomic constraints. Namely, the Legendre transform turns Lagrangian systems with nonholonomic constraints into unconstrained Hamiltonian systems with singular Hamilton function
Fichier principal
Vignette du fichier
hamiltonian-structures.pdf (231.33 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01398500 , version 1 (17-11-2016)

Identifiants

Citer

T. S. Ratiu, O. G. Smolyanov. Hamiltonian Structures in the Quantum Theory of Hamilton–Dirac Systems. Доклады Академии Наук / Doklady Mathematics, 2015, 91 (1 ), pp.68 - 71. ⟨10.1134/S1064562415010214⟩. ⟨hal-01398500⟩

Collections

TDS-MACS
38 Consultations
143 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More