Covariant Angular Momentum Analysis and Analytic Continuation

The "little group" decomposition of a two-particle scattering amplitude is carried out using covariant variables throughout. The general covariant expression for the amplitude reproduces, where appropriate, the $O\left(3\right)\mathrm{}$ and $O(2, 1)$ expansions. In the limit of zero momentum transfer, for unequal masses, it goes over correctly to an expansion in the functions of the two-dimensional Euclidean group.