TY - JOUR

T1 - Mass renormalization in nonrelativistic quantum electrodynamics

AU - Hiroshima, Fumio

AU - Spohn, Herbert

N1 - Funding Information:
The authors thank K. R. Ito for useful comments and a careful reading of the paper. F.H. thanks the kind hospitality of TU München in 2003. F.H. also thanks Grant-in-Aid 13740106 for Encouragement of Young Scientists and Grant-in-Aid for Science Reserch (C) 15540191 from MEXT for financial support.

PY - 2005/4

Y1 - 2005/4

N2 - In nonrelativistic quantum electrodynamics the charge of an electron equals its bare value, whereas the self-energy and the mass must 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 is well known, if m denotes the bare mass and meff the mass computed from the theory, to order α one has meff m=1+ (8α3π) log (1+ 1 2 (Λ/m)) +O (α2) which suggests that meff m= (Λ/m)8α3π for small α. If correct, in order α2 the leading term should be 1 2 ((8α3π) log (Λ/m)) 2. To check this point we expand meff m to order α2. The result is √Λ/m as leading term, suggesting a more complicated dependence of meff on m.

AB - In nonrelativistic quantum electrodynamics the charge of an electron equals its bare value, whereas the self-energy and the mass must 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 is well known, if m denotes the bare mass and meff the mass computed from the theory, to order α one has meff m=1+ (8α3π) log (1+ 1 2 (Λ/m)) +O (α2) which suggests that meff m= (Λ/m)8α3π for small α. If correct, in order α2 the leading term should be 1 2 ((8α3π) log (Λ/m)) 2. To check this point we expand meff m to order α2. The result is √Λ/m as leading term, suggesting a more complicated dependence of meff on m.

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U2 - 10.1063/1.1852699

DO - 10.1063/1.1852699

M3 - Article

AN - SCOPUS:17444388904

VL - 46

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

M1 - 042302

ER -