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 |
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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
Local symmetries and the Noether identities in the Hamiltonian framework. / Deriglazov, A. A.; Evdokimov, K. E.
In: International Journal of Modern Physics A, Vol. 15, No. 25, 10.10.2000, p. 4045-4067.Research output: Contribution to journal › Article
}
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 -