Massless Particles in Arbitrary Dimensions

Abstract

Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group ${\tilde{G}}_n={\widetilde{SO}}_0(2,n)$ are investigated for $n\ge 2$. It is found that, for space-time dimensions $n\ge 3$, the situation is quite similar to the one of the n=4 case for $S_n$-massless representations of the n-De Sitter group ${\widetilde{SO}}_0(2,n-1)$. These representations are the restrictions of the singletons of ${\tilde{G}}_n$. The main difference is that they are not contained in the tensor product of two UIRs with the same sign of energy when n>4, whereas it is the case for another kind of massless representation. Finally some examples of Gupta-Bleuler triplets are given for arbitrary spin and $n\ge 3$.

33 pages, LaTeX2e. To be published in Reviews in Math. Phys

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