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Arnold Neumaier
Nov4-06, 03:26 PM
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