Vertex functions and generalized normal-ordering by triple systems in non-linear spinor field models

TL;DR

This paper explores the role of triple systems and generalized normal-ordering in non-linear spinor field models, deriving vertex functions and discussing symmetry effects and running coupling constants.

Contribution

It introduces a novel approach using triple products to derive vertex functions and extend symmetry notions in non-linear spinor field models.

Findings

Derived the BCS interaction using triple systems.

Connected symmetry enlargement to regular vertex functions.

Outlined effects of running coupling constants on local interactions.

Abstract

Triple systems are closely related to Yang-Baxter symmetries. Utilizing a non-parameter-dependent triple product, we derive the BCS interaction. The enlargement of the notion of symmetry leads in some sense to a regular vertex function. The connection to the effect of running coupling constants is outlined, which leads to the recently discussed anisotropic effective local interactions. Furthermore, a discussion of the physical nature of q-symmetries is given.