Gauge Model With Extended Field Transformations in Euclidean Space

TL;DR

This paper explores an SO(4) gauge invariant model with extended field transformations in four-dimensional Euclidean space, analyzing the decomposition of fields and their transformation properties, and extending the approach to SO(5) in five dimensions.

Contribution

It introduces a novel extended field transformation framework for SO(4) gauge models and provides a detailed decomposition of fields into irreducible components, applicable also to higher dimensions.

Findings

Decomposition of reducible fields into irreducible SO(4) components.

Analysis of gauge transformations mixing different spin fields.

Extension of the approach to SO(5) in five-dimensional space.

Abstract

An SO(4) gauge invariant model with extended field transformations is examined in four dimensional Euclidean space. The gauge field is $(A^\mu)^{\alpha\beta} = 1/2 t^{\mu\nu\lambda} (M^{\nu\lambda})^{\alpha\beta}$ where $M^{\nu\lambda}$ are the SO(4) generators in the fundamental representation. The SO(4) gauge indices also participate in the Euclidean space SO(4) transformations giving the extended field transformations. We provide the decomposition of the reducible field $t^{\mu\nu\lambda}$ in terms of fields irreducible under SO(4). The SO(4) gauge transformations for the irreducible fields mix fields of different spin. Reducible matter fields are introduced in the form of a Dirac field in the fundamental representation of the gauge group and its decomposition in terms of irreducible fields is also provided. The approach is shown to be applicable also to SO(5) gauge models in five dimensional Euclidean space.