The Renormalized Electron Mass in Non-Relativistic Quantum Electrodynamics

Details The Renormalized Electron Mass in Non-Relativistic Quantum Electrodynamics The Renormalized Electron Mass in Non-Relativistic Quantum Electrodynamics

2005-07-18

arxiv.org/abs/math-ph/0507043v1

J. Funct. Anal., 243 (2), 426 - 535 (2007).

Physics

Mathematical Physics

AMS LaTeX, 101 pages

Scientific paper

This work addresses the problem of infrared mass renormalization for a scalar electron in a translation-invariant model of non-relativistic QED. We assume that the interaction of the electron with the quantized electromagnetic field comprises a fixed ultraviolet regularization and an infrared regularization parametrized by $\sigma>0$. For the value $p=0$ of the conserved total momentum of electron and photon field, bounds on the renormalized mass are established which are uniform in $\sigma\to0$, and the existence of a ground state is proved. For $|p|>0$ sufficiently small, bounds on the renormalized mass are derived for any fixed $\sigma>0$. A key ingredient of our proofs is the operator-theoretic renormalization group using the isospectral smooth Feshbach map. It provides an explicit, finite algorithm that determines the renormalized electron mass at $p=0$ to any given precision.

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