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 P: n/a Igor Khavkine wrote: > Arnold Neumaier wrote: > >>Igor Khavkine wrote: > >>>A term that, when added to the Lagrangian, only change the action by a >>>constant is called, in various contexts, a boundary term, a total >>>derivative, or a total divergence. >> >>The action for a translation invariant system must be translation >>invariant, and then the total divergence does not change the action >>(proper behavior at infinity assumed). > > > In the example (a single free non-relativistic particle), the action > does change under a boost of the particle path, of which the action is > a functional. However, it changes by an amount that depends only on the > boundary conditions (which are fixed, and perhaps also the integration > time interval, which is also fixed) and not on the particle path (which > is varied). Thus the equations of motion that are obtained from the > action by varying the particle path are still the same, regardless of > the applied boost. Yes, and I meant to say (behind what I actually wrote) that in this situation even the action is unchanged, since for a translation invariant action the resulting boundary conditions (which always follow from the action) are such that the integral of a total divergence vanishes automatically. Arnold Neumaier