04-406 F. Hiroshima and K. R. Ito

Mass Renormalization in Non-relativistic Quantum Electrodynamics with spin 1/2 (85K, Latex) Dec 9, 04

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Abstract. The effective mass $\mass$ of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff $\La$ and the bare mass $m$ in nonrelativistic QED with spin $\han$ is investigated. Analytic properties of $\mass$ in coupling constant $e$ are shown and explicit forms of constants $a_1(\La/m)$ and $a_2(\La/m)$ depending on $\La/m$ such that $$\mass/m =1 + a_1(\La/m) e^2+ a_2(\La/m) e^4+ {\mathcal O}(e^6)$$ are given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants $b_1,b_2, c_1$ and $c_2$ such that $$\d b_1\leq \liml \frac{a_1(\La/m)}{\log (\La/m)}\leq b_2,\ \ \ -c_1\leq \liml \frac{a_2(\La/m)}{(\La/m)^2}\leq -c_2.$$ In particular $a_2(\La/m)$ does not diverges as $\pm [\log(\La/m)]^2$ but $-(\La/m)^2$.

Files: 04-406.src( 04-406.keywords , MassRen.tex )