English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove the existence of the operator product expansion (OPE) in EuclideanYang-Mills theories as a short-distance expansion, to all orders inperturbation theory. We furthermore show that the Ward identities of theunderlying gauge theory are reflected in the OPE; especially, the OPE of anarbitrary number of gauge-invariant composite operators only involvesgauge-invariant composite operators. Moreover, we derive recursion relationswhich allow to construct the OPE coefficients, the quantum BRST differentialand the quantum antibracket order by order in perturbation theory, startingfrom the known free-theory objects. These relations are completely finite fromthe start, and do not need any further renormalisation as is usually the casein other approaches. Our results underline the importance of the OPE as ageneral structure underlying quantum field theories. The proofs are obtainedwithin the framework of the Wilson-Wegner-Polchinski-Wetterich renormalisationgroup flow equations, and generalise similar results recently obtained forscalar field theories [J. Holland and S. Hollands, Commun. Math. Phys. 336(2015) 1555; J. Holland and S. Hollands, J. Math. Phys. 56 (2015) 122303].Combining their results with our recursion formula, we also obtainassociativity of the OPE coefficients.

All-order existence of and recursion relations for the operator product expansion in Yang-Mills theory