### Abstract

The asymptotic behavior of the effective mass meff(Λ) of the so-called Nelson model in quantum field theory is considered, where Λ is an ultraviolet cutoff parameter of the model. Let m be the bare mass of the model. It is shown that for sufficiently small coupling constant α of the model, meff(Λ)/m can be expanded as meff(Λ)/m=1+n=1∞an(Λ)α2n. A physical folklore is that an(Λ)=O(logΛ(n-1)) as Λ→∞. It is rigorously shown that 0<limΛ→∞a1(Λ)<C, C1≤limΛ→∞a2(Λ)/logΛ≤C2 with some constants C, C1, and C2.

Original language | English |
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Article number | 4760105 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 2017 |

DOIs | |

Publication status | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

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## Cite this

Hiroshima, F., & Osawa, S. (2017). Mass Renormalization in the Nelson Model.

*International Journal of Mathematics and Mathematical Sciences*,*2017*, [4760105]. https://doi.org/10.1155/2017/4760105