  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.
