🚀 go-pugleaf

In article <MATT.92Nov8111138@physics.berkeley.edu> matt@physics.berkeley.edu writes:

>Um, not to get offensive about this, but...
>
>Even ordinary path integrals make me a bit nervous sometimes; I
>occasionally have trouble keeping myself under control so that I don't
>jump up, screaming "What's the measure?"  I can usually manage to do
>this by telling myself comforting lies about how the path integral is
>really the limit of a well-defined integral on a lattice as the
>lattice spacing is taken to zero, and by ignoring the fact that the
>measure diverges in this limit.

It's nice to hear a real physicist admit to worries along these
lines.  It's even nicer to find out how they calm themselves down: "This
seemingly meaningless expression is simply the limit of a well-defined
quantity as the lattice spacing goes to zero.  Does the limit exist?
That's not a physics question, that's MATHEMATICS."  :-)


I don't see any good reason why integrating over spaces of metrics is
more or less intimidating than integrating over spaces of other sorts of
fields.  The integral one claims to be doing in Yang-Mills theory is
an integral over a nasty infinite-dimensional stratified space
just like the space of metrics modulo diffeomorphisms.  Perturbative
renormalizability does not necessarily have much to do with whether
these integrals make sense, though it does let you pretend to calculate them.