Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-03
J.Phys.A40:11083-11092,2007
Physics
High Energy Physics
High Energy Physics - Theory
14 pages. Published version. Introduction has been rewritten, the rest part is the same as before
Scientific paper
10.1088/1751-8113/40/36/008
We analyze a singular theory with first class constraints of an arbitrary stage. Relation among the formulations of the constrained system in terms of complete and extended Hamiltonians is clarified. We replace the extended Hamiltonian $H_{ext}$ by an improved one. The improved Hamiltonian has the same structure as $H_{ext}$ (higher stage constraints enter into the Hamiltonian in the manifest form), but, in contrast to $H_{ext}$, it arises as the complete Hamiltonian for some Lagrangian $\tilde L$, called the extended Lagrangian. This implies, in particular, that all the quantities appearing in the improved Hamiltonian have a clear meaning in the Dirac framework. $\tilde L$ is obtained in a closed form in terms of quantities of the initial formulation $L$. The formulations with $L$ and $\tilde L$ turn out to be equivalent. As an application of the formalism, we found local symmetries of $\tilde L$ in a closed form. All the constraints of $L$ turn out to be gauge symmetry generators for $\tilde L$. The procedure is illustrated with an example of a model with fourth-stage constraints.
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