Some properties of constraints in theories with degenerate Lagrangians
type: Item
instance of: scholarly article
title: Some properties of constraints in theories with degenerate Lagrangians
zbMATH Open document ID: 0582.70021
DOI: 10.1007/BF01017038
author: B. George
published in: Theoretical and Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: 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 Hamiltonian are calculated. By means of Noether's theorem 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. If follows from the analysis of the functional arbitrariness in the solutions of the Hamilton equations that such primary constraints must be first-class constraints.
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 3932460
zbMATH Keywords: finite number of degrees of freedom
zbMATH Keywords: Poisson brackets of primary constraints
zbMATH Keywords: linear differential operators
zbMATH Keywords: Lagrangian constraints
zbMATH Keywords: existence
zbMATH Keywords: second-class constraints
zbMATH Keywords: canonical Hamiltonian
zbMATH Keywords: Noether's theorem
zbMATH Keywords: invariance of the action
zbMATH Keywords: first-class constraints
MaRDI profile type: Publication
cites work: Q4095928
cites work: Constrained dynamics. With applications to Yang-Mills theory, general relativity, classical spin, dual string model
cites work: Constraints in Covariant Field Theories
cites work: Der kanonische Formalismus in entarteten Fällen
cites work: Canonical formalism for degenerate Lagrangians
full work available at URL: https://doi.org/10.1007/bf01017038
OpenAlex ID: W2087176388
description: scientific article; zbMATH DE number 3932460