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arXiv · 2605.16172

Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills

M. M. Amaral·V. E. R. Lemes
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Abstract

In this work, we construct a BRST-exact quartet mechanism in $SU(3)$ Yang-Mills theory in the Landau gauge. The quartet sector is cohomologically trivial in the standard vacuum, ensuring equivalence to pure Yang-Mills theory. The transformation rules carry both commutator and anticommutator structures, enlarging the field content from eight to nine degrees of freedom. Working in a prescribed Cartan-oriented background (compatible with the classical equations of motion), the theory induces a mass matrix reproducing the distinct $i$-particle propagator structure of earlier replica models without explicit breaking terms. To respect the BRST doublet theorem, we separate background generation from observable cohomology. Introducing a background-equivariant covariant Cartan frame, we show the filtered $i$-particle bilinear is the lowest perturbative component of an all-orders off-shell BRST cocycle. Despite the complex poles of elementary propagators, its leading two-point function retains a K\"all\'en--Lehmann representation with a real positive threshold and positive spectral density. The fully quantized action provides a consistent framework for renormalizability, establishing a systematic mechanism for recovering $i$-particle propagators and identifying BRST-controlled composite observables from a BRST-exact quartet extended to $SU(3)$.

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M. M. Amaral, V. E. R. Lemes. 2026-05-15. Background-Equivariant BRST Observables and i-Particle Propagators from an Auxiliary Quartet in SU(3) Yang-Mills. https://arxiv.org/abs/2605.16172

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