Premium
Dirac Brackets in Constrained Dynamics
Author(s) -
Ibort Alberto,
de Leon Manuel,
Marrero Juan C.,
de Diego David Martin
Publication year - 1999
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/(sici)1521-3978(199906)47:5<459::aid-prop459>3.0.co;2-e
Subject(s) - holonomic constraints , mathematics , constraint (computer aided design) , holonomic , dirac (video compression format) , manifold (fluid mechanics) , first class constraint , hamiltonian mechanics , hamiltonian (control theory) , simple (philosophy) , bracket , poisson bracket , lagrangian , algebra over a field , classical mechanics , pure mathematics , computer science , lie algebra , geometry , physics , mathematical optimization , symplectic geometry , quantum mechanics , artificial intelligence , philosophy , phase space , engineering , symplectic representation , epistemology , mechanical engineering , symplectic manifold , neutrino
An unified geometric description of various Dirac brackets for regular and singular lagrangians with holonomic or non‐holonomic constraints is presented. Such unified picture relies only on two simple physical arguments: “classical complementarity principle” and “principle of deterministic evolution”. The appropriate geometrization of these principles allows to construct a recursive constraint algorithm that eventually produces a maximal final state manifold where a well defined dynamics exists, naturally equipped with a Dirac bracket such that the dynamics is hamiltonian with respect to it. A classification of constraints in first and second class as envisaged by Dirac emerges also naturally from this picture. The Dirac brackets constructed show explicitly the existence of classical anomalies for such lagrangian theories since in general they do not verify Jacobi's identity. Such features are discussed using a variety of examples.