  We consider how the continuous spin representation (CSR) of the Poincare
group in four dimensions can be generated by dimensional reduction. The
analysis uses the front-form little group in five dimensions, which must yield
the Euclidean group E(2), the little group of the CSR. We consider two cases,
one is the single spin massless representation of the Poincare group in five
dimensions, the other is the infinite component Majorana equation, which
describes an infinite tower of massive states in five dimensions. In the first
case, the double singular limit j,R go to infinity, with j/R fixed, where R is
the Kaluza-Klein radius of the fifth dimension, and j is the spin of the
particle in five dimensions, yields the CSR in four dimensions. It amounts to
the Inonu-Wigner contraction, with the inverse K-K radius as contraction
parameter. In the second case, the CSR appears only by taking a triple singular
limit, where an internal coordinate of the Majorana theory goes to infinity,
while leaving its ratio to the KK radius fixed.

High Energy Physics - Theory