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The operator product expansion converges in perturbative field theory

Hollands, Stefan and Kopper, Christoph 2012. The operator product expansion converges in perturbative field theory. Communications in Mathematical Physics 313 (1) , pp. 257-290. 10.1007/s00220-012-1457-4

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We show, within the framework of the massive Euclidean ϕ4-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 oper- ators 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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Springer
ISSN: 0010-3616
Last Modified: 10 Oct 2017 13:32

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