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The Renormalized Electron Mass in Non-Relativistic Quantum Electrodynamics | | Volker Bach
; Thomas Chen
; Juerg Froehlich
; Israel Michael Sigal
; | | Date: |
18 Jul 2005 | | Subject: | Mathematical Physics MSC-class: 81T16 | math-ph math.MP | | Abstract: | 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 $sigma o0$, 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. | | Source: | arXiv, math-ph/0507043 | | Services: | Forum | Review | PDF | Favorites | |
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