 03471 Fumio Hiroshima and Herbert Spohn
 Mass renormalization in nonrelativistic QED
(65K, latex)
Oct 17, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. In nonrelativistic QED the charge of an electron equals its bare
value, whereas the selfenergy and the mass have to be
renormalized. In our contribution we study perturbative mass
renormalization, including second order in the fine structure
constant $\alpha$, in the case of a single, spinless electron. As
well known, if $m$ denotes the bare mass and $\mass$ the mass
computed from the theory, to order $\alpha$ one has
$$\frac{\mass}{m} =1+\frac{8\alpha}{3\pi} \log(1+\half (\Lambda/m))+O(\alpha^2)$$
which suggests that $\mass/m=(\Lambda/m)^{8\alpha/3\pi}$ for small
$\alpha$. If correct, in order $\alpha^2$ the leading term should
be $\displaystyle \half ((8\alpha/3\pi)\log(\Lambda/m))^2$. To
check this point we expand $\mass/m$ to order $\alpha^2$. The
result is $\sqrt{\Lambda/m}$ as leading term, suggesting a more
complicated dependence of $m_{\mathrm{eff}}$ on $m$.
 Files:
03471.src(
03471.keywords ,
mass.tex )