Helicity of spin-extended chiral particles

Abstract

The helicity of a free massless relativistic particle, ${\chi }^o=\mathbf{s}.\mathbf{p}/|\mathbf{p}|$, is generalized, for a particle in an electromagnetic field, to $\chi =\mathbf{s}.\mathbf{p}/\mathcal{E}$, where $\mathcal{E}$ is the modified kinetic energy. Both ${\chi }^o$ and $\chi$ coincide and are conserved for minimal coupling (gyromagnetic ratio $g=0$) but are different and neither of them is conserved when the coupling is non-minimal, $g\ne 0$, generating non-zero effective mass. For a chiral particle with $g=2$ in a constant electric field both helicities converge asymptotically to the same value. Helicity is also conserved for minimal gravitational coupling.

Published version, slightly extended. 18 pages, 4 figures