In the Lagrangian formulation of Classical Mechanics, we have the freedom to add a total time derivative of an arbitrary function Λ to the Lagrangian:
L→L+dΛdt.
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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