Generalization of the Gell-Mann formula for sl(5, R) and su(5) algebras

TL;DR

This paper extends the Gell-Mann formula to be universally applicable for all representations of sl(5,R) and su(5) algebras by utilizing a group manifold framework involving SO(5) and Spin(5).

Contribution

A new generalized Gell-Mann formula for sl(5,R) and su(5) that works across all representations, overcoming previous limitations.

Findings

Generalized formula valid for all representations

Applicable to sl(5,R) and su(5) algebras

Uses group manifold framework involving SO(5) and Spin(5)

Abstract

The so called Gell-Mann formula expresses the Lie algebra elements in terms of the corresponding Inonu-Wigner contracted ones. In the case of sl(n, R) and su(n) algebras contracted w.r.t. so(n) subalgebras, the Gell-Mann formula is generally not valid, and applies only in the cases of some algebra representations. A generalization of the Gell-Mann formula for sl(5,R) and su(5) algebras, that is valid for all representations, is obtained in a group manifold framework of the SO(5) and/or Spin(5) group.