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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 to the theory of functions that depend on coordinate
and resolution . In the simplest case such field theory turns out to be a
theory of fields defined on the affine group ,
, which consists of dilations and translation of
Euclidean space. The fields are constructed using the
continuous wavelet transform. The parameters of the theory can explicitly
depend on the resolution . The proper choice of the scale dependence
makes such theory free of divergences by construction.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
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