Continuous Spin Representation from Contraction of the Conformal Algebra

Abstract

In this paper, we discuss the Inönü-Winger contraction of the conformal algebra. We start with the light-cone form of the Poincaré algebra and extend it to write down the conformal algebra in $d$ dimensions. To contract the conformal algebra, we choose five dimensions for simplicity and compactify the third transverse direction in to a circle of radius $R$ following Kaluza-Klein dimensional reduction method. We identify the inverse radius, $1/R$, as the contraction parameter. After the contraction, the resulting representation is found to be the continuous spin representation in four dimensions. Even though the scaling symmetry survives the contraction, but the special conformal translation vector changes and behaves like the four-momentum vector. We also discussed the generalization to $d$ dimensions.

Accepted for Publication in the Journal of Mathematical Physics

References in corpus (5)

• Elementary particles with continuous spin
• Light-cone continuous-spin field in AdS space
• Twistorial and space-time descriptions of massless infinite spin (super)particles and fields
• Pauli-Lubanski limit and stress-energy tensor for infinite-spin fields
• Group contractions and its consequences upon representations of different spatial symmetry groups