  We identify momentum/helicity probability amplitudes for the photon and find
their relativistic transformation properties. We also find their behaviour
under space inversion and time reversal. The discussion begins with a review of
the unitary, irreducible representations of the Poincare group for massless
particles. The little group, the set of Lorentz transformations that leave the
momentum unchanged, is distinctly different for massless particles compared to
the little group of rest frame rotations for a massive particle. We give a
physical interpretation of the little group for a massless particle. The
explicit forms of the Wigner rotations for general rotations and boosts are
given. In normalized superpositions of the basis vectors, we identify the
momentum/helicity probability amplitudes, show their probability interpretation
and find their transformation properties. We see that position eigenvectors for
the photon are not possible, not because of their masslessness but because of
their limited helicity spectrum. Instead, to have a measure of localization for
the photon, we use the expectations of the electromagnetic field strength
operators in a coherent state with a mean photon number of unity. In the
construction of the polarization vectors appearing in the field strengths, we
see the connection between gauge invariance and Lorentz covariance.

Quantum Physics;High Energy Physics - Theory