Massless High-spin Representations of Extended Poincaré Algebra

Abstract

All physical phenomena in the four-dimensional spacetime are invariant under the Poincaré group. The Standard Model of fundamental interactions, Electroweak theory, and Quantum Chromodynamics are required to be invariant under Poincaré group.  Any possible extension of the Poincaré group hints to the existence of a new physics beyond the Standard Model. In  particular, the supersymmetric extension of the Poincaré group predicts the existence of new particles that are supersymmetric partners of the elementary particles of the Standard Model: leptons, quarks, W and Z bosons and gluons. In a recently suggested high-spin extension of the Poincaré group, new massless particles of increasing spins are predicted to exist. In that respect we are interested in investigating a massless representation of the Poincaré algebra that has high-spin states. The massless states are described by  the helicity operator, which has only two polarisations equal to the components of spin along the direction of motion, as it takes place for photons and gravitons.  This means that not all of the 2s+1 spin magnetic quantum states exist and  the spin operator is not defined anymore.  In order to eliminate the spin operator from a massless representation and ensure  that only helicity operator is included  into the representations, Schwinger suggested that new non-commuting coordinates should be defined. We investigate the uncertainty relations that follow from non-commutativity of these new coordinates. It is the average wavelength of a massless particle that sets the scale of the coordinate uncertainty.