Sunday, 22 November 2015

classical mechanics - What's the name of the symmetry $ L to L + frac{d Lambda}{dt}$?


In the Lagrangian formulation of Classical Mechanics, we have the freedom to add a total time derivative of an arbitrary function $\Lambda$ to the Lagrangian:


$$ L \to L + \frac{d \Lambda}{dt} . $$


Does this symmetry of the Lagrangian have any particular name?



Answer



Some authors call that a gauge transformation of the Lagrangian function. Others, don't give any specific name and may object to the previous one.


For a reference for the former denomination, see for instance F. Scheck, Mechanics, Springer, 2010.


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