The operator product expansion converges in perturbative field theory

Details The operator product expansion converges in perturbative field theory The operator product expansion converges in perturbative field theory

2011-05-17

arxiv.org/abs/1105.3375v3

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 39 pages, v2: minor changes, v3: further minor changes

Scientific paper

We show, within the framework of the Euclidean $\phi^4$-quantum field theory in four dimensions, that the Wilson operator product expansion (OPE) is not only an asymptotic expansion at short distances as previously believed, but even converges at arbitrary finite distances. Our proof rests on a detailed estimation of the remainder term in the OPE, of an arbitrary product of composite fields, inserted as usual into a correlation function with further "spectator fields". The estimates are obtained using a suitably adapted version of the method of renormalization group flow equations. Convergence follows because the remainder is seen to become arbitrarily small as the OPE is carried out to sufficiently high order, i.e. to operators of sufficiently high dimension. Our results hold for arbitrary, but finite, loop orders. As an interesting side-result of our estimates, we can also prove that the "gradient expansion" of the effective action is convergent.

Affiliated with

Also associated with

No associations

Rating

The operator product expansion converges in perturbative field theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The operator product expansion converges in perturbative field theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The operator product expansion converges in perturbative field theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727793