A new class of particle in 2 + 1 dimensions

In two spatial dimensions, spin characterizes how particle states re-phase under changes of frame that leave their momentum and energy invariant. Massless particles can in principle have non-trivial spin in this sense, but all existing field theories only describe the trivial case. This letter presents a field theory for a massless particle with non-trivial physical spin. These particles are the (2+1)(2+1)-dimensional analogues of “continuous-spin” particles in 3+13+1 dimensions, but here they have only two real degrees of freedom, related by parity. They can be understood as massless generalizations of anyons, but are simpler in key respects.