规范变换对Birkhoff系统对称性的影响

研究Birkhoff系统规范变换对其Noether对称性、Lie对称性和Mei对称性的影响.在一定条件下，Noether对称性和守恒量不改变.Lie对称性和Hojaman守恒量仍保持不变.Mei对称性和新型守恒量可能变化，得到了Mei对称性和新型守恒量保持不变的条件.举例说明结果的应用.关键词：Birkhoff系统规范变换对称性守恒量

Effects of gauge transformations on symmetries of Birkhoffian system

The effects of gauge transformation on Noether symmetry, Lie symmetry and Mei symmetry of a Birkhoff system are studied. Under certain conditions, the system can keep its Noether symmetry and conserved quantity. The Lie symmetry and Hojman conserved quantity of the system will still remain unchanged. The Mei symmetry and a new-type conserved quantity of the system may very, and the conditions under which the Mei symmetry and the new-type conserved quantity will remain are obtained. An example is given to illustrate the application of the results.