Mass Renormalization in the Nelson Model
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...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2017/4760105 |
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| author | Fumio Hiroshima Susumu Osawa |
| author_facet | Fumio Hiroshima Susumu Osawa |
| author_sort | Fumio Hiroshima |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-533ad6eef7424290b9058d3b40b11b63 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-533ad6eef7424290b9058d3b40b11b632025-02-03T06:07:44ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252017-01-01201710.1155/2017/47601054760105Mass Renormalization in the Nelson ModelFumio Hiroshima0Susumu Osawa1Faculty of Mathematics, Kyushu University, Fukuoka 819-0385, JapanFaculty of Science, Department of Mathematics, Hokkaido University, Sapporo, Hokkaido 060-0810, JapanThe 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.http://dx.doi.org/10.1155/2017/4760105 |
| spellingShingle | Fumio Hiroshima Susumu Osawa Mass Renormalization in the Nelson Model International Journal of Mathematics and Mathematical Sciences |
| title | Mass Renormalization in the Nelson Model |
| title_full | Mass Renormalization in the Nelson Model |
| title_fullStr | Mass Renormalization in the Nelson Model |
| title_full_unstemmed | Mass Renormalization in the Nelson Model |
| title_short | Mass Renormalization in the Nelson Model |
| title_sort | mass renormalization in the nelson model |
| url | http://dx.doi.org/10.1155/2017/4760105 |
| work_keys_str_mv | AT fumiohiroshima massrenormalizationinthenelsonmodel AT susumuosawa massrenormalizationinthenelsonmodel |