Dependence of the off-energy-shellTmatrix on the total three-momentum

Abstract

The Bakamjian-Thomas form of relativistic potential theory is used to derive a constraint on the off-energy-shell two-body $T$ matrix elements. This is an equation which specifies the dependence of these matrix elements on the total three-momentum. While other formulations lead to different constraints, it is argued that this one is the most convenient. The distinction between this formula and the (irrelevant) notion of Lorentz transforming an off-energy-shell matrix element is discussed. A critical comparison is made with several formulas which have appeared in the literature in connection with the problem of scattering a $\pi$ meson by a nucleus.