Scale-Dependent Functions, Stochastic Quantization and Renormalization
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions φ(b) ∊ L²(Rd) to the theory of functions that depend on coordinate b and resoluti...
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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Scale-Dependent Functions, Stochastic Quantization and Renormalization / M.V. Altaisky // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
oai:nasplib.isofts.kiev.ua:123456789-146180 |
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oai:nasplib.isofts.kiev.ua:123456789-1461802025-02-23T17:17:50Z Scale-Dependent Functions, Stochastic Quantization and Renormalization Altaisky, M.V. We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions φ(b) ∊ L²(Rd) to the theory of functions that depend on coordinate b and resolution a. In the simplest case such field theory turns out to be a theory of fields φa(b,·) defined on the affine group G: x′ = ax+b, a > 0, x, b ∊ Rd, which consists of dilations and translation of Euclidean space. The fields φa(b,·) are constructed using the continuous wavelet transform. The parameters of the theory can explicitly depend on the resolution a. The proper choice of the scale dependence g = g(a) makes such theory free of divergences by construction The author is thankful to the referee for useful comments and references. 2006 Article Scale-Dependent Functions, Stochastic Quantization and Renormalization / M.V. Altaisky // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37E20; 42C40; 81T16; 81T17 https://nasplib.isofts.kiev.ua/handle/123456789/146180 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions φ(b) ∊ L²(Rd) to the theory of functions that depend on coordinate b and resolution a. In the simplest case such field theory turns out to be a theory of fields φa(b,·) defined on the affine group G: x′ = ax+b, a > 0, x, b ∊ Rd, which consists of dilations and translation of Euclidean space. The fields φa(b,·) are constructed using the continuous wavelet transform. The parameters of the theory can explicitly depend on the resolution a. The proper choice of the scale dependence g = g(a) makes such theory free of divergences by construction |
| format |
Article |
| author |
Altaisky, M.V. |
| spellingShingle |
Altaisky, M.V. Scale-Dependent Functions, Stochastic Quantization and Renormalization Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Altaisky, M.V. |
| author_sort |
Altaisky, M.V. |
| title |
Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_short |
Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_full |
Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_fullStr |
Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_full_unstemmed |
Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_sort |
scale-dependent functions, stochastic quantization and renormalization |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| citation_txt |
Scale-Dependent Functions, Stochastic Quantization and Renormalization / M.V. Altaisky // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT altaiskymv scaledependentfunctionsstochasticquantizationandrenormalization |
| first_indexed |
2025-07-22T04:13:29Z |
| last_indexed |
2025-07-22T04:13:29Z |
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1838318993664901120 |