A nonassociative operator decomposition of strongly interacting quantum fields

TL;DR

This paper proposes a nonassociative operator decomposition for strongly interacting quantum fields, revealing quantum corrections from bracket permutations and drawing parallels to dimensional transmutation effects.

Contribution

It introduces a novel nonassociative decomposition method for quantum field operators, advancing algebraic approaches to strongly interacting quantum fields.

Findings

Quantum corrections arise from bracket permutations.

Corrections are comparable to those from dimensional transmutation.

The approach offers new algebraic tools for quantum field theory.

Abstract

Working towards an algebra for operators of strongly interacting quantum fields, a nonassociative decomposition of field operators is proposed. In the demonstrated case, quantum corrections appear from the possible bracket permutations. A similarity of these corrections, as compared to corrections from dimensional transmutation, is considered.