 04406 F. Hiroshima and K. R. Ito
 Mass Renormalization in Nonrelativistic Quantum Electrodynamics with spin 1/2
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Dec 9, 04

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Abstract. The effective mass $\mass$ of the the PauliFierz 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 $(\La/m)^2$.
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