Improved extended Hamiltonian and search for local symmetries

Abstract

We analyze a structure of the singular Lagrangian L with first and second class constraints of an arbitrary stage. We show that there exist an equivalent Lagrangian (called the extended Lagrangian L̃) that generates all the original constraints on second stage of the Dirac–Bergmann procedure. The extended Lagrangian is obtained in closed form through the initial one. The formalism implies an extension of the original configuration space by auxiliary variables. Some of them are identified with gauge fields supplying local symmetries of L̃. As an application of the formalism, we found closed expression for the gauge generators of L̃ through the first class constraints. It turns out to be much more easy task as those for L. All the first class constraints of L turn out to be the gauge symmetry generators of L̃. By this way, local symmetries of L with higher order derivatives of the local parameters decompose into a sum of the gauge symmetries of L̃.