Title: Loop Representation of Wigner's Little Groups,
Abstract: Wigner's little groups are the subgroups of the Lorentz group whose
transformations leave the momentum of a given particle invariant. They thus
define the internal space-time symmetries of relativistic particles. These
symmetries take different mathematical forms for massive and for massless
particles. However, it is shown possible to construct one unified
representation using a graphical description. This graphical approach allows us
to describe vividly parity, time reversal, and charge conjugation of the
internal symmetry groups. As for the language of group theory, the two-by-two
representation is used throughout the paper. While this two-by-two
representation is for spin-1/2 particles, it is shown possible to construct the
representations for spin-0 particles, spin-1 particles, as well as for
higher-spin particles, for both massive and massless cases. It is shown also
that the four-by-four Dirac matrices constitute a two-by-two representation of
Wigner's little group.