Heinz J Rothe and Klaus D Rothe 2003 J. Phys. A: Math. Gen. 36 1671 doi:10.1088/0305-4470/36/6/311
Lagrange versus symplectic algorithm for constrained systems
Heinz J Rothe and Klaus D Rothe
Show affiliationsThe systematization of the purely Lagrangian 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 Lagrangian constraints in the theory. We apply this approach to a general Lagrangian 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 Lagrangian 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.
- PACS
- MSC
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81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
- Subjects
- Dates
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Issue 6 (14 February 2003)
Received 16 August 2002, in final form 20 November 2002
Published 29 January 2003
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Lagrange versus symplectic algorithm for constrained systems
Heinz J Rothe and Klaus D Rothe 2003 J. Phys. A: Math. Gen. 36 1671
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