Re: non-locality of the equation of motion

From: Arnold Neumaier (Arnold.Neumaier_at_univie.ac.at)
Date: 12/30/04 

Date: Thu, 30 Dec 2004 17:47:37 +0000 (UTC)

? ? wrote:

> What about the second question, how can we handle high derivatives in the
> equation of motion, can we get it from some variantion of Euler-Lagrange
> equation from some kind of action? or there is some reason to rule out this
> kind of possibility.

On the classical level, higher derivatives cause no formal problems,
one can form the variational equations as always. there might be
problems with causality (=3D symmetric hyperbolicity), however.
These problems become worse (and apparently untractable) in the
quantum case.

In a k derivative theory with k>1, one can always introduce new fields
for the k-1 first derivatives, and add terms to the acrtion that give
as variation their defining equations. Thus one can reduce any theory
to an equivalent one with only first derivbatives in the action.
The problems appear when trying to go from the Lagrangian picture to
the Hamiltonian - then one gets similar diffculties as for gauge
theories.

I don't know much more about this.

Arnold Neumaier