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Author Altaisky, Mikhail V.
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2006-04-24
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics
Subject Keyword High Energy Physics - Theory ♦ physics:hep-th
Abstract 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 $\phi(b)\in L^2({\mathbb R}^d)$ 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 $\phi_a(b,\cdot)$ 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 $\phi_a(b,\cdot)$ 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.
Description Reference: SIGMA 2:046,2006
Educational Use Research
Learning Resource Type Article


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