It would be some interest, given the crucial role this feature plays in the structure of the theory, to understand better how it works. One method of doing this would be to formulate a general, practical characterization of having ``gauge freedom associated with diffeomorphisms, and, up to this freedom, a well-posed initial-value formulation". That is, we would like a precise definition of this feature, a definition that, on the one hand, is applicable to a wide class of partial differential equations; and that, on the other, is easy to apply, in practice, to members of that class. This is what we do here.
As far as I am aware, the only viable
physical theories whose equations satisfy our characterization of this
feature are, essentially, general relativity and special relativity.
It is possible to invent certain systems of equations that do satisfy
our criterion, but these do not seem to underlie physical theories.
Are there any other candidate theories - either already in existence, or
even ``reasonable" theories based on systems of equations invented solely for
this purpose? If none can be found, then
might we be able to formulate a no-go theorem along these lines?
Such a theorem might offer some insight into the structure of
relativistic theories of physics.
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Lecture notes: revised version, 8.V.2003
Video for lecture 2 not available - computer crash
Slides for for lectures 1, 2, 3 not available
Copyright 10.X.2002 by P.T.Chrusciel, A.Chopin, and R.Geroch