Four-potentials and Maxwell Field Tensors from SL(2,C) Spinors as Infinite-Momentum/Zero-Mass Limits of their Massive Counterparts

Four $SL(2,C)$ spinors are considered within the framework of Wigner's little groups which dictate internal space-time symmetries of relativistic particles. It is indicated that the little group for a massive particle at rest is $O(3)$, while it is $O(3)$-like for a moving massive particle. The little group becomes like $E(2)$ in the infinite-momentum/zero-mass limit. Spin-$\frac{1}{2}$ particles are studied in detail, and the origin of the gauge degrees of freedom for massless particles is clarified. There are sixteen different combinations of direct products of two $SL(2,C)$ spinors for spin-1 and spin-0 particles. The state vectors for the $O(3)$ and $O(3)$-like little groups are constructed. It is shown that in the infinite-momentum/zero-mass limit, these state vectors become scalars, four-potentials and the Maxwell field tensor. It is revealed that the Maxwell field tensor so obtained corresponds to some of the state vectors constructed by Weinberg in 1964.