Self-Interacting Complex Scalar Quantum Field Theories

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Abstract
Conditions for a local, essentially nonlinear, complex scalar field theory to admit vacuum, one-quantum, and two-quantum particle-antiparticle stationary states are derived with the Rayleigh-Ritz procedure for functionalities. It is shown that only so-called Class-A theories, for which the self-interaction energy density divided by the absolute value of the field squared is uniformly bounded for all values of the field, admit wholly acceptable one-quantum and two-quantum particle-antiparticle stationary states. The Class-A theories appear to be effectively linear, with no observable interaction between the two quanta in the case of the two-quantum particle-antiparticle stationary states.