Scale-dependent stochastic quantization

Based on the wavelet-defined multiscale random noise proposed in [Doklady Physics 2003, v.48, 478], a multiscale version of the stochastic quantization procedure is considered. A new type of the commutation relations emerging from the multiscale decomposition of the operator-valued fields is derivedComment: Talk at FFP6 International Conference, Udine, Italy, Sep 2004. LaTeX, 7 pages, 5 eps figure

Wavelet-Based Quantum Field Theory

The Euclidean quantum field theory for the fields φΔx(x), which depend on both the position x and the resolution Δx, constructed in SIGMA 2 (2006), 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments

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 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 constructio

On scale invariance and Ward identities in statistical hydrodynamics

Considering the incompressible viscid fluid driven by random force $f(t,r)$, we have found out the existence of such nontrivial correlators, that the characteristic functional of alluded stochastic process has the symmetry features, as if no random force is present. Based on this fact, two sets of Ward identities related with the scale invariance of Navier-Stokes equations are constructed. These identities are important for renormalization in functional-integral approach to hydrodynamical turbulence. Besides, they impose some restriction on turbulence spectra. The particular case of degenerating turbulence with energy spectrum $E(k,t)\sim k^{-3}t^{-2}$ is also under consideration