Scale-Dependent Functions, Stochastic Quantization and Renormalization
| dc.creator | Altaisky, Mikhail V. | |
| dc.date | 2006-04-24 | |
| dc.date.accessioned | 2026-07-07T12:20:27Z | |
| dc.date.available | 2026-07-07T12:20:27Z | |
| dc.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 $ϕ(b)\in L^2({\mathbb R}^d)$ 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 $ϕ_a(b,\cdot)$ defined on the affine group $G:x'=ax+b$, $a>0,x,b\in {\mathbb R}^d$, which consists of dilations and translation of Euclidean space. The fields $ϕ_a(b,\cdot)$ 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. | |
| dc.description | Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/hep-th/0604170 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0604170 | |
| dc.identifier | SIGMA 2:046,2006 | |
| dc.identifier | doi:10.3842/SIGMA.2006.046 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213073 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Scale-Dependent Functions, Stochastic Quantization and Renormalization | |
| dc.type | text |