Helicity of spin-extended chiral particles

• The helicity of chiral particles coupled minimally is conserved.
• For non-minimal coupling the helicity may not be conserved.
• Motion in electric field provides example when helicity is not conserved.
• When coupled non-minimally the helicity is not boost-invariant.
• When coupled minimally to gravitation, helicity is conserved.

The helicity of a free massless relativistic particle, χo=s⋅p/|p|χo=s⋅p/|p|, is generalized, for a particle in an electromagnetic field, to χ=s⋅p/Eχ=s⋅p/E where EE is energy. Both χoχo and χ   coincide and are conserved for minimal coupling (gyromagnetic ratio g=0g=0) but are different and neither of them is conserved when the coupling is non-minimal, g≠0g≠0, generating non-zero effective mass. For a chiral particle with g=2g=2 in a constant electric field both helicities converge asymptotically to the same value. Helicity is also conserved for minimal gravitational coupling.