  Einstein's photo-electric effect allows us to regard electromagnetic waves as
massless particles. Then, how is the photon helicity translated into the
electric and magnetic fields perpendicular to the direction of propagation?
This is an issue of the internal space-time symmetries defined by Wigner's
little group for massless particles. It is noted that there are three
generators for the rotation group defining the spin of a particle at rest. The
closed set of commutation relations is a direct consequence of Heisenberg's
uncertainty relations. The rotation group can be generated by three two-by-two
Pauli matrices for spin-half particles. This group of two-by-two matrices is
called SU(2), with two-component spinors. The direct product of two spinors
leads to four states leading to one spin-0 state and one spin-1 state with
three sub-states. The SU(2) group can be expanded to another group of
two-by-two matrices called SL(2,c), which serves as the covering group for the
group of Lorentz transformations. In this Lorentz-covariant regime, it is
possible to Lorentz-boost the particle at rest to its infinite-momentum or
massless state. Also in this SL(2,c) regime, there are four spin states for
each particle, as in the case of the Dirac equation. The direct product of two
SL(2,c) spinors thus leads sixteen states. Among them, four of them can be used
for the electromagnetic four-potential, and six for the Maxwell tensor. The
gauge degree of freedom is shown to be a Lorentz-boosted rotation. The
polarization of massless neutrinos is interpreted as a consequence of the gauge
invariance.
