F. Hiroshima and K. R. Ito
Mass Renormalization in Non-relativistic Quantum Electrodynamics with spin 1/2
(85K, Latex)

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 $-(\La/m)^2$.