Lagrange versus Symplectic Algorithm for Constrained Systems

Details Lagrange versus Symplectic Algorithm for Constrained Systems Lagrange versus Symplectic Algorithm for Constrained Systems

2002-08-15

arxiv.org/abs/hep-th/0208106v1

J.Phys.A36:1671-1682,2003

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX

Scientific paper

10.1088/0305-4470/36/6/311

The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left zero-modes as there are Lagrangean constraints in the theory. We apply this approach to a general Lagrangean in the first order formulation and show how the seemingly overdetermined set of equations is solved for the velocities by suitably extending W to a rectangular matrix. As a byproduct we thereby demonstrate the equivalence of the Lagrangean approach to the traditional Dirac-approach. By making use of this equivalence we show that a recently proposed symplectic algorithm does not necessarily reproduce the full constraint structure of the traditional Dirac algorithm.

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