Ground State of a Model in Relativistic Quantum Electrodynamics with a Fixed Total Momentum

A system of a single relativistic electron interacting with the quantized electromagnetic field is considered. We mainly study this system with a fixed total momentum p — This system is called the Dirac polaron. We analyze the lowest energyE(p) of the Dirac polaron, and derive some properties: concavity, symmetricity, and the inverse energy inequality E(p) ≤ E(0), p ∈ R. Furthermore, we consider the existence of the ground state of the Dirac polaron. We show that the Dirac polaron has a ground state under a condition which includes an infrared regularization condition and an ultraviolet cutoff. This ensures that the relativistic dressed one electron state exists.