Study of a gauge invariant local composite fermionic field

TL;DR

This paper investigates a gauge invariant local composite fermionic field within a Yang-Mills framework, demonstrating its renormalizability and analyzing its algebraic properties in the context of quantum field theory.

Contribution

It introduces a new gauge invariant composite fermionic field and proves its renormalizability in a Yang-Mills theory with fermionic matter.

Findings

Proved the renormalizability of the model to all orders.

Analyzed the Ward identities and algebraic structure.

Established the consistency of the composite fermionic field.

Abstract

In this work, we study a gauge invariant local non-polynomial composite spinor field in the fundamental representation in order to establish its renormalizability. Similar studies were already done in the case of pure Yang-Mills theories where a local composite gauge invariant vector field was obtained and an invariant renormalizable mass term could be introduced. Our model consists of a massive Euclidean Yang-Mills action with gauge group $SU(N)$ coupled to fermionic matter in the presence of an invariant spinor composite field and quantized in the linear covariant gauges. The whole set of Ward identities is analysed and the algebraic proof of the renormalizability of the model is obtained to all orders in a loop expansion.