Renormalisation of a diagonal formulation of first order Yang-Mills theory

TL;DR

This paper investigates the renormalization process of a diagonal formulation of Yang-Mills theory using BRST symmetry, demonstrating its renormalizability to all orders in the Landau gauge.

Contribution

It introduces a diagonal matrix-propagator formulation of Yang-Mills theory and proves its all-order renormalizability via BRST identities.

Findings

BRST identities ensure recursive renormalizability

Diagonal propagator simplifies renormalization analysis

Renormalization holds to all perturbative orders

Abstract

We study the BRST renormalization of an alternative formulation of the Yang-Mills theory, where the matrix-propagator of the gluon and the complementary fields is diagonal. This procedure involves scalings as well as non-linear mixings of the fields and sources. We show, in the Landau gauge, that the BRST identities implement a recursive proof of renormalizability to all orders.