Functional self-similarity and renormalization group symmetry in mathematical physics

@article{Kovalev1999FunctionalSA,
  title={Functional self-similarity and renormalization group symmetry in mathematical physics},
  author={V. F. Kovalev and D. V. Shirkov},
  journal={Theoretical and Mathematical Physics},
  year={1999},
  volume={121},
  pages={1315-1332}
}
  • V. F. KovalevD. V. Shirkov
  • Published 1 October 1999
  • Physics
  • Theoretical and Mathematical Physics
The results from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the regular algorithm for finding renormalization group-type symmetries using the contemporary theory of Lie groups of transformations. 
View on Springer
arxiv.org
19 Citations
Methods Citations
1

19 Citations

Renormalization group symmetry method and gas dynamics

Renorm-group symmetry for functionals of boundary value problem solutions

Recent advances in generalizing the renorm-group algorithm for boundary value problems of mathematical physics and the related concept of the renorm-group symmetry, previously formulated with…

Analyzing jump phenomena and stability in nonlinear oscillators using renormalization group arguments

We study the stability of a damped Duffing oscillator by employing a renormalization group method for solving nonlinear differential equations. This approach is direct and makes the study of the…

A Hint of renormalization

An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical…

Renormalization group symmetry and initial value problem for shallow water equations

Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups

An extended Lie group analysis method is provided that is also applicable to partial differential equations and makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.

New class of symmetries and exact solution to the unsteady equations of adiabatic gas dynamics

One Property of the Renormalization Group Operator

We use an isotropic ferromagnet as an example to show that the renormalization group operator can be interpreted as an evolution operator for a system of spins evolving with an increase of the…

Renormalization group and Lienard systems of differential equations

Autonomous Lienard systems, which constitute a huge family of periodic motions, exhibit limit cycle behaviour in certain cases and centres in others. In the literature, the signature for the…

Can renormalization group flow end in a big mess

References

SHOWING 1-10 OF 48 REFERENCES

RENORMALIZATION GROUP IN MODERN PHYSICS

Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of…

A geometrical formulation of the renormalization group method for global analysis II: Partial differential equations

It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations…

Renormalization Group in Mathematical Physics and Some Problems of Laser Optics

An original approach to constructing special type symmetries for boundary value problems, RENORMGROUP SYMMETRIES, is reviewed here. It is applied to a system of geometric optics equations. New…

Renormalization group symmetries in problems of nonlinear geometrical optics

We construct renormalization group symmetries in the geometrical optics approximation for the boundary value problem of the system of equations describing the propagation of strong radiation in a…

Group and renormgroup symmetry of a simple model for nonlinear phenomena in optics, gas dynamics, and plasma theory

Renormalization group analysis for singularities in the wave beam self-focusing problem

A singular solution of the boundary value problem for the system of equations describing wave beam self-focusing is investigated by constructing renormalization group symmetries. New analytic…

The analytic approach in quantum chromodynamics

In a new “renormalization invariant analytic formulation” of calculations in quantum chromodynamics, the renormalization group summation is correlated with the analyticity with respect to the square…

Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based…

Group and Renormgroup Symmetry of Quasi-Chaplygin Media

Results of renormgroup analysis of a quasi-Chaplygin system of equations are presented. Lie-Backlund symmetries and corresponding invariant solutions for different “Chaplygin” functions are obtaine...

Temperature dependence of the QCD coupling

We present a one-loop calculation of a gauge invariant QCD β-function. Using both momentum and temperature renormalization group equations we investigate the running coupling in the magnetic sector…