Abstract:
The Poisson brackets of primary constraints are expressed by means of linear differential
operators in terms of Lagrangian constraints. A criterion for the existence in a theory of
second-class constraints is proposed in the framework of the Lagrangian formalism. The
Poisson brackets of primary constraints with the canonical Harniltonian are calculated. By
means of Noether's theorem, Part II, it is shown that invariance of the action with respect
to transformations with arbitrary functions of the time leads to primary constraints that
are in involution with one another and with the canonical Hamiltonian, at least in the weak
sense. It follows from the analysis of the functional arbitrariness in the solutions of the
Hamilton equations that such primary constraints must be first-class constraints.
Citation:
V. V. Nesterenko, A. M. Chervyakov, “Some properties of constraints in theories with degenerate Lagrangians”, TMF, 64:1 (1985), 82–91; Theoret. and Math. Phys., 64:1 (1985), 701–707
\Bibitem{NesChe85}
\by V.~V.~Nesterenko, A.~M.~Chervyakov
\paper Some properties of constraints in theories with degenerate Lagrangians
\jour TMF
\yr 1985
\vol 64
\issue 1
\pages 82--91
\mathnet{http://mi.mathnet.ru/tmf4904}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=815099}
\zmath{https://zbmath.org/?q=an:0582.70021}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 64
\issue 1
\pages 701--707
\crossref{https://doi.org/10.1007/BF01017038}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1985AYT5900009}
Linking options:
https://www.mathnet.ru/eng/tmf4904
https://www.mathnet.ru/eng/tmf/v64/i1/p82
This publication is cited in the following 7 articles:
V. V. Kozlov, “On Dirac's generalized Hamiltonian dynamics”, Russian Math. Surveys, 79:4 (2024), 649–681
José F. Carińena, “Theory of Singular Lagrangians”, Fortschr. Phys., 38:9 (1990), 641
V V Nesterenko, “Singular Lagrangians with higher derivatives”, J. Phys. A: Math. Gen., 22:10 (1989), 1673
C Batlle, J Gomis, J M Pons, N Roman-Roy, “Lagrangian and Hamiltonian constraints for second-order singular Lagrangians”, J. Phys. A: Math. Gen., 21:12 (1988), 2693
José F. Cariñena, Carlos López, Narciso Román-Roy, “Origin of the Lagrangian constraints and their relation with the Hamiltonian formulation”, Journal of Mathematical Physics, 29:5 (1988), 1143
V. V. Nesterenko, “Calculation of static interquark potential in a string model in a timelike gauge”, Theoret. and Math. Phys., 71:2 (1987), 504–511
Jose F. Cariñena, Carlos Lopez, Narciso Roman-Roy, “Geometric study of the connection between the Lagrangian and Hamiltonian constraints”, Journal of Geometry and Physics, 4:3 (1987), 315
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