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

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

2006-06-09

arxiv.org/abs/math-ph/0606029v4

Physics

Mathematical Physics

Scientific paper

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 $\mathbf{p}$ -- This system is called the Dirac polaron. We analyze the lowest energy $E(\mathbf{p})$ of the Dirac polaron, and derive some properties: concavity, symmetricity, and the inverse energy inequality $E(\mathbf{p})\leq E(0)$, $\mathbf{p}\in\mathbb{R}^3$. Furthermore, we consider the existence of the ground state of the Dirac polaron model. We show that the Dirac polaron model 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.

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