nonlocal effective action by integrating out fermions
- From: "Tom" <buenzlth@xxxxxx>
- Date: Sun, 22 Jan 2006 21:59:46 +0000 (UTC)
Starting with the pathintegral of a gauge theory, say Qed to keep it
simple, and (Grassmann-)integrating out a quadratic fermion action you
end up with a determinant of the Dirac Operator essentialy. It is
always said that we get a nonlocal contribution to the action that way.
det(D) = exp(ln[det(D)]) = exp(tr[ln(D)])
The trace in the last expression is essentialy an integration over
spacetime. So it seems to me, we have a contribution to the effective
action that is local in the sense the the action is a spacetime
integral over a Lagrange-density.
I really seem to missunderstand something here.
Tom
.
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