Abstract
In the framework of the Lagrangian formalism the partial differential equation under study does not define univocally the Lagrangian density. In this paper we obtain a necessary and sufficient consistency condition over the ansatz that assures the invariance of the collective coordinates (CCs) equations under the change of equivalent Lagrangian densities. When this condition is not fulfilled we show explicitly that different equations of CCs may emerge from equivalent Lagrangian densities and a good agreement between the CCs and the partial differential equations is not expected.
| Original language | English |
|---|---|
| Article number | 065204 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 44 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 11 Feb 2011 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Modelling and Simulation
- Statistics and Probability
Cite this
Equivalent Lagrangian densities and invariant collective coordinates equations. / Zamora-Sillero, Elías; Shapovalov, Aleksandr Vasilievich.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 44, No. 6, 065204, 11.02.2011.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Equivalent Lagrangian densities and invariant collective coordinates equations
AU - Zamora-Sillero, Elías
AU - Shapovalov, Aleksandr Vasilievich
PY - 2011/2/11
Y1 - 2011/2/11
N2 - In the framework of the Lagrangian formalism the partial differential equation under study does not define univocally the Lagrangian density. In this paper we obtain a necessary and sufficient consistency condition over the ansatz that assures the invariance of the collective coordinates (CCs) equations under the change of equivalent Lagrangian densities. When this condition is not fulfilled we show explicitly that different equations of CCs may emerge from equivalent Lagrangian densities and a good agreement between the CCs and the partial differential equations is not expected.
AB - In the framework of the Lagrangian formalism the partial differential equation under study does not define univocally the Lagrangian density. In this paper we obtain a necessary and sufficient consistency condition over the ansatz that assures the invariance of the collective coordinates (CCs) equations under the change of equivalent Lagrangian densities. When this condition is not fulfilled we show explicitly that different equations of CCs may emerge from equivalent Lagrangian densities and a good agreement between the CCs and the partial differential equations is not expected.
UR - http://www.scopus.com/inward/record.url?scp=79551655950&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79551655950&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/44/6/065204
DO - 10.1088/1751-8113/44/6/065204
M3 - Article
VL - 44
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 6
M1 - 065204
ER -