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

Abstract

The effective mass $\mass$ of the the Pauli-Fierz Hamiltonain with ultraviolet cutoff $\Lambda$ 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 $a_1(\Lambda /m)$ and $a_2(\Lambda /m)$ depending on $\Lambda /m$ 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 $a_2(\Lambda /m)$ does not diverges as $\pm [\log (\Lambda /m){]}^2$ but $-(\Lambda /m{)}^2$.

References in corpus (3)

• Enhanced Binding in non-relativistic QED
• Mass renormalization in nonrelativistic QED
• The increase of Binding Energy and Enhanced Binding in Non-Relativistic QED

Cited by in corpus (2)

• Effective dynamics of an electron coupled to an external potential in non-relativistic QED
• Mass Renormlization in the Nelson Model