### Abstract

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.

Original language | English |
---|---|

Article number | 042302 |

Journal | Journal of Mathematical Physics |

Volume | 46 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 1 2005 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*46*(4), [042302]. https://doi.org/10.1063/1.1852699

**Mass renormalization in nonrelativistic quantum electrodynamics.** / Hiroshima, Fumio; Spohn, Herbert.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 46, no. 4, 042302. https://doi.org/10.1063/1.1852699

}

TY - JOUR

T1 - Mass renormalization in nonrelativistic quantum electrodynamics

AU - Hiroshima, Fumio

AU - Spohn, Herbert

PY - 2005/4/1

Y1 - 2005/4/1

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.

UR - http://www.scopus.com/inward/record.url?scp=17444388904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17444388904&partnerID=8YFLogxK

U2 - 10.1063/1.1852699

DO - 10.1063/1.1852699

M3 - Article

VL - 46

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

M1 - 042302

ER -