Massless Particles in Arbitrary Dimensions

TL;DR

This paper explores properties of massless representations of the conformal and de Sitter groups in various dimensions, revealing similarities and differences with the four-dimensional case and providing examples of Gupta-Bleuler triplets.

Contribution

It extends the analysis of massless representations to arbitrary dimensions, highlighting their structure and differences from lower-dimensional cases, and introduces examples of Gupta-Bleuler triplets.

Findings

Massless representations in higher dimensions resemble the 4D case for certain types.

These representations are restrictions of singletons of the conformal group.

Examples of Gupta-Bleuler triplets are provided for arbitrary spin and 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 $n\ge2$. It is found that, for space-time dimensions $n\ge3$, 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 $n\ge3$.