Dmitrii V. Shirkov

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 on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.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 on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.

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 general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view we present a simple derivation of the renorm-group (RG) in QFT “liberated” from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare “different” RG’s.

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 solutions to the laser beam self-focusing problem are presented.

Dreamland with Classic Higgs Field, Dimensional Reduction and All That

This text, on the one hand, is related to the talk delivered at the conference “Gauge Fields. Yesterday, Today, Tomorrow” dedicated to the 70th anniversary of Andrei Slavnov; on the other—in the form of a fairy tale—it summarizes some results of the research performed after this Fest, mainly due to discussion around the talk.

Introduction to the Theory of Quantized Fields

This site is also available in the following languages: Български Català Deutsch Ελληνικά English Español Français Hrvatski Italiano Norsk/Bokmål Polski Português Русский Slovensky Svenska ( ) ( ) Start by marking “Introduction to the Theory of Quantized Fields” as Want to Read: Want to Read saving... Want to Read. Currently Reading. Read. Introduction to the Th by D.V. Shirkov. Other editions. The quantum theory that one nds agrees with the usual picture of canonical quantization that one learns in standard eld theory. The quantum theory also comes with a representation of the inhomogeneous Lorentz group (the Poincar ́e group) that arises from an analytic continuation of the quantization of the Euclidean group. Thus the two fundamental points of view mesh to one. We rst investigate a special case that relates to the Gaussian path integral and the free quantum eld. We then give the general construction that applies for bosonic non-linear elds. Introduction to Quantum Field Theory. 24 ... In this chapter we give a dierent perspective on the ordinary quantum theory of a single spinless, positive msss-m particle on Rd−1. In this edition we have rewritten the chapters that discuss the methods of continuous integration and the renormalization group, which are two topics in theory that have become extremely important in recent years. We have also reworked and supplemented the sections on the complete Green functions.This work was done in an atmosphere of friendly advice and fruitful discussions with our colleagues from the Steklov Mathematical Institute of the USSR Academy of Sciences and of the Laboratory of Theoretical Physics of the Joint Institute of Nuclear Studies, to whom we are extremely grateful. Introduction To The Theory Of Quantized Fields