Open AccessA counterexample of Dirac's conjecture for a system with a higher-order singular Lagrangian
Author(s) -
Aimin Li,
Zhang Xiao-Pei,
Ziping Li
Publication year - 2003
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.52.1057
Subject(s) - noether's theorem , counterexample , mathematical physics , mathematics , hamiltonian (control theory) , homogeneous space , conjecture , lagrangian , phase space , canonical form , pure mathematics , physics , quantum mechanics , discrete mathematics , mathematical optimization , geometry
The extended canonical Noether identities derived from an extended action in the phase space for a system with a higher-order singular Lagrangian are formulated.Based on the canonical symmetries of generalized constrained Hamiltonian systems, a counterexample to a conjecture of Dirac is given. Using the canonical first Noether theorem and canonical Noether identities and the extended canonical Noether identities, we have shown that Dirac's conjecture fails for a system with a higher-order singular Lagrangian in which there is no linearization of constraint in our treatment.