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 nonrelativistic 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
