Mass Renormalization in Non-relativistic Quantum Electrodynamics with Spin 1/2

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

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