The renormalized electron mass in non-relativistic quantum electrodynamics

• Published in: Journal of functional analysis Vol. 243; no. 2; pp. 426 - 535
• Main Authors: Bach, Volker, Chen, Thomas, Fröhlich, Jürg, Sigal, Israel Michael
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.02.2007
• Subjects: Mass renormalization; Quantum electrodynamics; Renormalization group methods; Spectral analysis; Renormalization group methods; Mass renormalization; Quantum electrodynamics; Spectral analysis
• ISSN: 0022-1236; 1096-0783
• DOI: 10.1016/j.jfa.2006.09.017

This work addresses the problem of infrared mass renormalization for a non-relativistic electron minimally coupled to the quantized electromagnetic field (the standard, translationally invariant system of an electron in non-relativistic QED). We assume that the interaction of the electron with the quantized electromagnetic field is subject to an ultraviolet regularization and an infrared regularization parametrized by σ > 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 σ → 0 , and the existence of a ground state is proved. For | p | > 0 sufficiently small, bounds on the renormalized mass are derived for any fixed σ > 0 . A key ingredient of our proofs is the operator-theoretic renormalization group based on the isospectral smooth Feshbach map. It provides an explicit, finite algorithm for determining the renormalized electron mass at p = 0 to any given precision.