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Inter-Particle Potentials in Non-Linear Quantum Field Theories

This research is concerned with the inter-particle potentials for few-particle bound state systems in a scalar model with a Higgs-like mediating field and QCD. The variational method, in a reformulated Hamiltonian formalism of QFT, is used to derive relativistic few particle wave equations and, consequently, the corresponding inter-particle potentials for stationary states of systems in question. The cubic and quartic contributions to the inter-particle potentials, in the non-relativistic limit, are expressed as multi-dimensional integrals. In the scalar Higgs-like model, when the mediator is massive, it is found that the non-linear terms modify the attractive Yukawa potential. In the case of QCD, the derived quark-antiquark potential is significantly affected by the non-linear terms and provides a signal of confinement.