Re: Nonuniqueness of actions

In article <[EMAIL PROTECTED]>, "Squark" <[EMAIL PROTECTED]> 
wrote:

> "Aaron Bergman" <[EMAIL PROTECTED]> wrote in message
> news:[EMAIL PROTECTED]
> > Let's say you're doing a path integral over some bosons and fermions.
> > The fermion path integral ends up being a Pfaffian of some operator on
> > bosonic fields. However, the Pfaffian is not usually a function on the
> > space of bosonic fields (reduced by gauge equivalence for gauge theories
> > or just in general for something like sigma model anomalies), rather it
> > is a section of a line bundle.
> 
> How come? Are you saying exp(iS_fermionic) take values in a line bundle?

Not quite. The path integral over the fermions gives something that's a 
section of a line bundle. Why is it a line bundle? Because it's a 
Pfaffian. The Pfaffian is the squar root of the determinant. There's 
necessarily a choice of sign there. As usual, locally this is easy, but 
globally you get a line bundle, not necessarily trivial.

> Also, does it mean one cannot have gauge anomalies without fermions?

Yes.

Aaron