Conformal invariance and conserved quantity of Lagrange systems under Lie point transformation

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Abstract
Conformal invariance and conserved quantities of Lagrange system under Lie point transformation are studied. Firstly, the definition of conformal invariance and determining equation for the Lagrange system are provided. Secondly, the relationship between the system’s conformal invariance and Lie symmetry are discussed; the necessary and sufficient condition on which the system’s conformal invariance would be Lie symmetry under the infinitesimal one-parameter point transformation group is deduced; and the conserved quantities of the system are given. Lastly, an illustration example is introduced.

Keywords:
Lagrange system /

Lie point transformation /

conformal invariance /

conserved quantity
Authors and contacts
Cai Jian-Le²,

Mei Feng-Xiang¹

(1)北京理工大学理学院，北京 100081; (2)杭州师范大学理学院，杭州 310018；北京理工大学理学院，北京 100081
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