A New Spin on Long-Range Interactions: Continuous Spin Particles and Predictions for their Interactions
Kinematically, massless particles in Lorentz-invariant theories are classified by a dimensionful "spin scale"ρ (2nd Casimir invariant) that characterizes helicity states' mixing under little group transformations. However, dynamics for particles with generic spin scale is poorly understood --- all known interacting theories’ massless modes have zero spin-scale (and hence exactly Lorentz-invariant helicity), and the powerful no-go theorems that exclude higher spins also presume a vanishing spin scale.
I will introduce a field theory for the general case of non-zero spin scale or "continuous spin" bosons and discuss its coupling to matter particles in a Lagrangian formalism. Remarkably, physical observables are well approximated by familiar theories at frequencies larger than ρ, with calculable and (so far) well behaved infrared deviations at low frequencies and long distances. For example, our recent work predicts specific ρ-dependent modifications to the Larmor formula and Compton scattering, laying the foundation for experimental tests of the photon's spin scale. I will also highlight open theoretical questions spurred by this work, including the localization of matter currents, the possibility of continuous spin analogues of gravity and non-Abelian gauge theories, and potential connections to the hierarchy problem.