Renormalization of SU(2) Yang-Mills theory with flow equations

Abstract : The goal of this work is a rigorous perturbative construction of the SU(2) Yang-Mills theory in four dimensional Euclidean space. The functional integration technique gives a mathematical basis for establishing the differential Flow Equations of the renormalization group for the effective action. While the introduction of momentum space regulators permits to give a mathematical definition of the Schwinger functions, the important difficulty of the approach is the fact that these regulators break gauge invariance. Thus the main part of the work is to prove at all loop orders the existence of the vertex functions and the restoration of the Slavnov-Taylor identities in the renormalised theory.
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Alexander Efremov. Renormalization of SU(2) Yang-Mills theory with flow equations. Mathematical Physics [math-ph]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLX050⟩. ⟨tel-01637943⟩

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