### Abstract

We study in the Hamiltonian framework the local transformations δ(ε)q(A)(τ) = Σ(k = 0)/([k]) δ(τ)/(k)ε(α)R((k))(α)(A)(q(B),q(C)) which leave invariant the Lagrangian action: δ(ε)S = div. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities have very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. The other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least ([k] + 1) stage. It is proven also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. The manifest form of the resulting generating function is obtained.

Original language | English |
---|---|

Pages (from-to) | 4045-4067 |

Number of pages | 23 |

Journal | International Journal of Modern Physics A |

Volume | 15 |

Issue number | 25 |

DOIs | |

Publication status | Published - 10 Oct 2000 |

### Fingerprint

### Keywords

- Hamiltonian systems with constraints
- Local symmetries

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics
- Astronomy and Astrophysics

### Cite this

*International Journal of Modern Physics A*,

*15*(25), 4045-4067. https://doi.org/10.1142/S0217751X00001890

**Local symmetries and the Noether identities in the Hamiltonian framework.** / Deriglazov, A. A.; Evdokimov, K. E.

Research output: Contribution to journal › Article

*International Journal of Modern Physics A*, vol. 15, no. 25, pp. 4045-4067. https://doi.org/10.1142/S0217751X00001890

}

TY - JOUR

T1 - Local symmetries and the Noether identities in the Hamiltonian framework

AU - Deriglazov, A. A.

AU - Evdokimov, K. E.

PY - 2000/10/10

Y1 - 2000/10/10

N2 - We study in the Hamiltonian framework the local transformations δ(ε)q(A)(τ) = Σ(k = 0)/([k]) δ(τ)/(k)ε(α)R((k))(α)(A)(q(B),q(C)) which leave invariant the Lagrangian action: δ(ε)S = div. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities have very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. The other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least ([k] + 1) stage. It is proven also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. The manifest form of the resulting generating function is obtained.

AB - We study in the Hamiltonian framework the local transformations δ(ε)q(A)(τ) = Σ(k = 0)/([k]) δ(τ)/(k)ε(α)R((k))(α)(A)(q(B),q(C)) which leave invariant the Lagrangian action: δ(ε)S = div. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities have very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. The other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least ([k] + 1) stage. It is proven also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. The manifest form of the resulting generating function is obtained.

KW - Hamiltonian systems with constraints

KW - Local symmetries

UR - http://www.scopus.com/inward/record.url?scp=0034633601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034633601&partnerID=8YFLogxK

U2 - 10.1142/S0217751X00001890

DO - 10.1142/S0217751X00001890

M3 - Article

AN - SCOPUS:0034633601

VL - 15

SP - 4045

EP - 4067

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 25

ER -