  We investigate two seemingly disjoint definitions of helicity, one commonly
used in particle physics, the other one used when studying bilinear covariants
of Clifford algebras. We can prove that the `mathematical' definition of
helicity implies its `physical' counterpart. As an unexpected application of
our result we show that the Hamiltonian describing the one-layer superconductor
Graphene is proportional to the trace of an operator that is used in the
`mathematical' definition of helicity.
