### 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.

Original language | English |
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Article number | 012907 |

Journal | Journal of Mathematical Physics |

Volume | 50 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*50*(1), [012907]. https://doi.org/10.1063/1.3068728

**Improved extended Hamiltonian and search for local symmetries.** / Deriglazov, A. A.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 50, no. 1, 012907. https://doi.org/10.1063/1.3068728

}

TY - JOUR

T1 - Improved extended Hamiltonian and search for local symmetries

AU - Deriglazov, A. A.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=59349118013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=59349118013&partnerID=8YFLogxK

U2 - 10.1063/1.3068728

DO - 10.1063/1.3068728

M3 - Article

VL - 50

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

M1 - 012907

ER -