Fermions from the gauge models ground state

TL;DR

This paper explores the quantization of U(1) and U(2) gauge theories near non-trivial vacuums, revealing that the ground state can be described as a massless Dirac field satisfying the Fermi-Dirac statistics, with implications for the Standard Model.

Contribution

It introduces a novel approach to gauge theory ground states using quaternionic functions, enabling a field description that incorporates fermionic properties and self-dual configurations.

Findings

Ground state described as a massless Dirac field.

Vacuum quantization allows for self-dual configurations.

Potential link to lepton sector of the Standard Model.

Abstract

We investigate the quantization of pure U(1) and U(2) gauge theories in the vicinity of non-trivial ground state in four-dimensional Euclidean space-time. The main goal is to make the simultaneous consideration of many vacuums possible. It is shown that Fueter (quaternion) analytic and anti analytic functions can be used as vacuum's collective coordinates. As a result the ground state describes not a single quasi particle, or finite number of such particles, but a field. This field satisfies the massless Dirac equation. This is not a contradiction because it is known that massless spinors can be quantized either as fermions or as bosons. We choose to quantize the vacuum anomalously (Fermi--Dirac). The anomalous quantization of the gauge fields ground state allows non-trivial (anti) self-dual configurations to exist. The possible connection to the lepton sector of the Standard Model is discussed.