Mathematical Analysis of a System of a Dirac Particle Interacting With a Quantum Electronagnetid Field

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(i)A Hamiltonian H of a quantum system of a Dirac particle interacting with a quantum electromagnetic field is described by a Dirac-Maxwell operator. The nonrelativistic limit of H is considered. It is proven that a scaled Hamiltonian H_c with a parameter c converges in the strong resolvent sense to the Pauli-Fierz Hamiltonian as c tends to infinity.(ii)Existence of a scaling limit of H which yields an effective Hamiltonian of the quantum system under consideration.(iii)Existence of the enhanced binding of a class of quantum systems in nonrelativisitc quantum field theory.