The Bogoluibov Renormalization Group in Theoretical and Mathematical Physics
نویسنده
چکیده
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmer-mann 70th birthday. The historical overview (Part 1) partially overlaps with corresponding text of my previous commemorative paper – see Ref. [61] in the list. At the same time second part includes some recent results in QFT (Sect. 2.1) and summarize (Sect. 2.4) an impressive progress of the " QFT renormalization group " application in mathematical physics.
منابع مشابه
Evolution of the Bogoluibov Renormalization Group
We start with a simple introduction into the renormalization group (RG) in quantum field theory and give an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT. Here, some fresh results are included. Then we turn to the remarkable proliferation of the RG ideas into various fields of physics. The last section summarize...
متن کاملA numerical renormalization group approach for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators
Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...
متن کاملTHE BOGOLIUBOV RENORMALIZATION GROUP Second English printing
We begin with personal notes describing the atmosphere of ”Bogoliubov renormalization group” birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its applicatio...
متن کاملTime-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملExact Renormalization Group Approach in Scalar and Fermionic Theories
As it is known (see an interesting review by Shirkov) the basic idea of the renormalization group (RG) was formulated in an article by Stueckelberg and Petermann. The existence of such group of transformations was related to the arbitrariness in the procedure of subtraction of ultraviolet divergencies in quantum electrodynamics. Functional equations for the propagators in the ultraviolet limit,...
متن کامل