On the ionization energy of the semi-relativistic Pauli-Fierz model for a single particle

Abstract

A semi-relativistic Pauli-Fierz model is defined by the sum of the free Hamiltonian $H_{\mathrm{f}}$ of a Boson Fock space, an nuclear potential $V$ and a relativistic kinetic energy: $$H=\sqrt{[\sigma \cdot (\mathbf{p}+e\mathbf{A}){]}^2+M^2}-M+V+H_{\mathrm{f}}.$$ Let $-e_0<0$ be the ground state energy of a semi-relativistic Schrödinger operator $$H_{\mathrm{p}}=\sqrt{{\mathbf{p}}^2+M^2}-M+V.$$ It is shown that the ionization energy $E^{\mathrm{ion}}$ of $H$ satisfies $$E^{\mathrm{ion}}\ge e_0>0$$ for all values of both of the coupling constant $e\in \mathbb{R}$ and the rest mass $M\ge 0$. In particular our result includes the case of M=0.

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