Field Theory for Stable and Unstable Particles

A completely covariant field theory is developed which includes both stable and unstable particle fields. Exact single-particle propagators for both the unstable and stable cases are derived for arbitrary spin in terms of matrix elements of the basic interaction. The free-particle approximation to these propagators does not contain the unphysical terms which are usually present in the propagators derived in the interaction picture. The relationship to the Lehmann spectral representation is established and general equations for the various renormalization constants are given. Based upon general considerations it is shown that in the limit of high momentum transfer an extra factor $t^{-2\mathrm{}}$ occurs in the cross section for 2-particle-to-2-particle scattering, more in line with experimental observations.