Masslessness in $n$-dimensions

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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

Scientific paper

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.

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