### 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 |

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### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

### Cite this

*International Journal of Mathematics and Mathematical Sciences*,

*2017*, [4760105]. https://doi.org/10.1155/2017/4760105

**Mass Renormalization in the Nelson Model.** / Hiroshima, Fumio; Osawa, Susumu.

Research output: Contribution to journal › Article

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

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TY - JOUR

T1 - Mass Renormalization in the Nelson Model

AU - Hiroshima, Fumio

AU - Osawa, Susumu

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=85021633353&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021633353&partnerID=8YFLogxK

U2 - 10.1155/2017/4760105

DO - 10.1155/2017/4760105

M3 - Article

AN - SCOPUS:85021633353

VL - 2017

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 4760105

ER -