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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2006 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2006
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146180 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Scale-Dependent Functions, Stochastic Quantization and Renormalization / M.V. Altaisky // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 27 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862529998782464000 |
|---|---|
| author | Altaisky, M.V. |
| author_facet | Altaisky, M.V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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
|
| first_indexed | 2025-11-24T02:39:12Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146180 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T02:39:12Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Altaisky, M.V. 2019-02-07T20:33:33Z 2019-02-07T20:33:33Z 2006 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 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Scale-Dependent Functions, Stochastic Quantization and Renormalization Article published earlier |
| spellingShingle | Scale-Dependent Functions, Stochastic Quantization and Renormalization Altaisky, M.V. |
| title | 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_short | Scale-Dependent Functions, Stochastic Quantization and Renormalization |
| title_sort | scale-dependent functions, stochastic quantization and renormalization |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146180 |
| work_keys_str_mv | AT altaiskymv scaledependentfunctionsstochasticquantizationandrenormalization |