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Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation |
| HUANG Wei-Li1,2, CAI Jian-Le2**
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1Department of Physics and Telecom Engineering, Hunan City University, Yiyang 413000
2College of Science, Hangzhou Normal University, Hangzhou 310018
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| Cite this article: |
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HUANG Wei-Li, CAI Jian-Le 2011 Chin. Phys. Lett. 28 110203 |
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Abstract Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.
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02.20.Sv
11.30.-j
45.20.Jj
03.50.-z
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Received: 15 July 2011
Published: 30 October 2011
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| PACS: |
02.20.Sv
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(Lie algebras of Lie groups)
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11.30.-j
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(Symmetry and conservation laws)
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45.20.Jj
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(Lagrangian and Hamiltonian mechanics)
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03.50.-z
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(Classical field theories)
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