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