Masslessness in $n$-dimensions

Abstract

We determine the representations of the ``conformal'' group ${\overline{SO}}_0(2,n)$, the restriction of which on the ``Poincaré'' subgroup ${\overline{SO}}_0(1,n-1).T_n$ are unitary irreducible. We study their restrictions to the ``De Sitter'' subgroups ${\overline{SO}}_0(1,n)$ and ${\overline{SO}}_0(2,n-1)$ (they remain irreducible or decompose into a sum of two) and the contraction of the latter to ``Poincaré''. 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.

34 pages, LaTeX2e, 1 figure. To be published in Reviews in Math. Phys

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