On Lorentz Invariant Complex Scalar Fields

Figure 3

Feynman diagrams in momentum space showing two possible processes for the Lorentz covariant Schrödinger theory when we introduce interaction terms that break Lorentz invariance. These two processes are kinematically forbidden for the Klein-Gordon theory subjected to analogous interaction terms. (a) An antiparticle (-particle) with momentum and energy decays into another antiparticle and two particles (-particles). The energies of the particles are and . We can represent this process by the following equation, . Note that the process (not shown in the picture) in which particles and antiparticles exchange roles, , is kinematically forbidden. (b) An antiparticle decays into a photon and a particle, . The processes (not shown in the picture) , , and are all kinematically forbidden.