非相对论性QED中的质量重整化
Mass renormalization in nonrelativistic QED
摘要：
在非相对论QED中，电子的电荷等于其裸值，而自能和质量必须重整化。在我们的贡献中，我们研究了微扰质量重整化，包括精细结构常数$α$中的二级，在单个无自旋电子的情况下，众所周知，如果$m$表示裸质量，$\mass$表示从理论计算的质量，为了$α$，我们有$$\frac{\mass}{m} =1+\frac{8α}{3π} \log(1+\half (Λ/m))+O(α^2)$$，这表明对于小$α$，$\mass/m=(Λ/m)^{8α/3π}$。如果正确，则在顺序$α^2$中，前导项应为$\displaystyle \half ((8α/3π)\log(Λ/m))^2$。为了检查这一点，我们将$\mass/m$展开为有序$α^2$。结果是$\sqrt{Λ/m}$作为主导项，表明$m_{\mathrm{eff}}$对$m$的依赖性更复杂。
英文摘要：
In nonrelativistic QED the charge of an electron equals its bare value, whereas the self-energy and the mass have to be renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine structure constant $α$, 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 $α$ one has $$\frac{\mass}{m} =1+\frac{8α}{3π} \log(1+\half (Λ/m))+O(α^2)$$ which suggests that $\mass/m=(Λ/m)^{8α/3π}$ for small $α$. If correct, in order $α^2$ the leading term should be $\displaystyle \half ((8α/3π)\log(Λ/m))^2$. To check this point we expand $\mass/m$ to order $α^2$. The result is $\sqrt{Λ/m}$ as leading term, suggesting a more complicated dependence of $m_{\mathrm{eff}}$ on $m$.
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