Extension of the Poincar\'e Symmetry and Its Field Theoretical Implementation

TL;DR

This paper introduces a novel algebraic extension of Poincaré symmetry, constructs a corresponding field theory, and explores its degrees of freedom, gauge invariance, and potential interactions.

Contribution

It presents a new algebraic extension of Poincaré symmetry and develops a field theoretical model based on this extension, including free Lagrangians and interaction possibilities.

Findings

Explicit free Lagrangians constructed

Analysis of degrees of freedom and gauge invariance

Discussion of potential interaction terms

Abstract

We define a new algebraic extension of the Poincar\'e symmetry; this algebra is used to implement a field theoretical model. Free Lagrangians are explicitly constructed; several discussions regarding degrees of freedom, compatibility with Abelian gauge invariance etc. are done. Finally we analyse the possibilities of interaction terms for this model.