相关论文: Scale-Dependent Functions, Stochastic Quantization…
Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the…
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier…
Renormalization group transformations for Schr\"odinger equation are performed in $\phi^4$ and in Yang-Mills theories. The dependence of the ground state wave functional on rapidly oscillating fields is found. For Yang-Mills theory, this…
The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation…
We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory. We use the results to calculate the renormalization functions $\beta$, $\gamma$, $\gamma_m$ of…
It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\phi,t]$ and the scale-dependent full effective action $\Gamma[\Phi,t]$ --in…
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an…
It is shown that Euclidean field theory with polynomial interaction, can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered with…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this…
We investigate the renormalization group flows of multicomponent scalar theories with $U(1)$ gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple,…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
The $\beta$ function for a scalar field theory describes the dependence of the coupling constant on the renormalization mass scale. This dependence is affected by the choice of regularization scheme. I explicitly relate the…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…
The regularization of quantum electrodynamics in the space of functions $\psi_a(x)$, which depend on both the position $x$ and the scale $a$, is presented. The scale-dependent functions are defined in terms of the continuous wavelet…
We develop the functional renormalization group formalism for a tensorial group field theory with closure constraint, in the case of an Abelian just renormalizable model with quartic interactions. The method allows us to obtain a closed but…
Following previous work by one of the authors [M.V.Altaisky, Unifying renormalization group and the continuous wavelet transform, Phys. Rev. D 93, 105043 (2016).], we develop a new approach to the renormalization group, where the effective…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…