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arXiv · 1611.08538

Mass Renormlization in the Nelson Model

Fumio Hiroshima·Susumu Osawa
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Abstract

The asymptotic behavior of the effective mass $m_{\rm eff}(Λ)$ 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, $m_{\rm eff}(Λ)/m$ can be expanded as $m_{\rm eff}(Λ)/m= 1+\sum_{n=1}^\infty a_n(Λ) α^{2n}$. A physical folklore is that $a_n(Λ)\sim [\log Λ]^{(n-1)}$ as $Λ\to \infty$. It is rigorously shown that $$0<\lim_{Λ\to\infty}a_1(Λ)<C,\quad C_1\leq \lim_{Λ\to\infty}a_2(Λ)/\logΛ\leq C_2$$ with some constants $C$, $C_1$ and $C_2$.

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Fumio Hiroshima, Susumu Osawa. 2017-06-21. Mass Renormlization in the Nelson Model. https://doi.org/10.1155/2017%2F4760105

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