Masslessness in $n$-dimensions

TL;DR

This paper classifies unitary irreducible representations of the conformal group in n-dimensions, examines their restrictions to subgroups like de Sitter, and discusses the concept of masslessness, highlighting differences from the 4-dimensional case.

Contribution

It provides a detailed analysis of conformal group representations in arbitrary dimensions and explores the notion of masslessness beyond four dimensions.

Findings

Classification of conformal group representations in n-dimensions.

Restrictions to de Sitter subgroups and their decompositions.

Comparison of massless representations in various dimensions.

Abstract

We determine the representations of the ``conformal'' group ${\bar{SO}}_0(2, n)$, the restriction of which on the ``Poincar\'e'' subgroup ${\bar{SO}}_0(1, n-1).T_n$ are unitary irreducible. We study their restrictions to the ``De Sitter'' subgroups ${\bar{SO}}_0(1, n)$ and ${\bar{SO}}_0(2, n-1)$ (they remain irreducible or decompose into a sum of two) and the contraction of the latter to ``Poincar\'e''. Then we discuss the notion of masslessness in $n$ dimensions and compare the situation for general $n$ with the well-known case of 4-dimensional space-time, showing the specificity of the latter.