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Topic: Renormalization

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	Acta Physica Slovaca, volume 52, December 2002, no.6
		The field theoretic renormalization group is applied to Kraichnan's model of a passive scalar quantity advected by the Gaussian velocity field with the pair correlation function $\propto\delta(t-t')/k^{d+\varepsilon}$.
		Renormalization group analysis is applied to the two-dimensional Navier--Stokes vorticity equation driven by a Gaussian random stirring.
		The standard demand for the quantum partition function to be invariant under the renormalization group transformation results in a general class of exact renormalization group equations, different in the form of the kernel.
	www.acta.sav.sk /acta02/no6/index.html (2000 words)

	Renormalization
		Renormalization (NB: also spelled "Renormalisation") is a mathematical inconsistency in quantum field theory that is so well established that one is forced to either accept it without question or to use it as an excuse for avoiding the study of interacting quantum field theory altogether.
		Renormalization can be summarised as follows: developing quantum field theory from first principles involves applying a process known as "quantization" to classical field theory.
		Renormalization, in short, consists of the turning of a blind eye to the mathematical inconsistencies of interacting field theory.
	www.cgoakley.demon.co.uk /qft/renorm.html (1198 words)

	Preface to Scaling and Renormalization...
		Historically, the subjects of renormalization in quantum field theory (as applied to particle physics) and in equilibrium critical behaviour have developed in parallel.
		As a result, the study of the subject rapidly becomes overladen with formalism, and the student, if he or she is lucky, has just about time to learn how to calculate the critical exponents of the Ising model in 4 minus epsilon dimensions before the course comes to an end.
		For the majority, whose goal is to understand how scaling and renormalization ideas might be applied to the rich variety of complex phenomena apparent in many other branches of the physical sciences, the main object is to learn the concepts, and the best way to do this is by covering as many examples as possible.
	www-thphys.physics.ox.ac.uk /users/JohnCardy/bookpreface.html (1762 words)

	The Renormalization Group (Site not responding. Last check: 2007-10-10)
		In the renormalization method, we use the computer to change the configurations in a way that is similar to moving away from the photograph.
		The second step is to determine the probability that characterizes the new configuration. Each cell is assumed to be independent of all the other cells and characterized only by the probability that the cell is occupied i.e.
		After one renormalization some of the original connecting paths are lost and some connecting paths not present in the original configuration are created.
	www.physics.udel.edu /wwwusers/jim/percolation/renormalization.htm (752 words)

	CERN Courier - Fifty years of the renormali - IOP Publishing - article
		Renormalization was the breakthrough that made quantum field theory respectable in the late 1940s.
		The most important feature of renormalization is that the calculation of physical quantities gives finite functions of new "renormalized" couplings (such as electron charge) and masses, all infinities being swallowed by the Z factors of the renormalization redefinition.
		However, from the mid-1950s the Renormalization Group Method to improve approximate solutions to QFT equations became a powerful tool for investigating singular behaviour in both the ultraviolet (higher energy) and infrared (lower energy) limits.
	www.cerncourier.com /main/article/41/7/14 (1737 words)

	Renormalization group - Wikipedia, the free encyclopedia
		In theoretical physics, renormalization group (RG) refers to a set of techniques and concepts related to the change of physics with the observation scale.
		Thus, the renormalization group is, in practice, a semigroup.
		Renormalized perturbation theory is the main technique associated to momentum-space RG.
	en.wikipedia.org /wiki/Renormalization_group (1943 words)

	Renormalization
		Renormalization, on the other hand, is a different process.\nRenormalization is required because, when standard perturbation theory\nis used, it is found that the photon has a divergent mass.
		Renormalization, on the other hand, is a different process.\nandgt; Renormalization is required because, when standard perturbation theory\nandgt; is used, it is found that the photon has a divergent mass.
		Renormalization, on the other hand, is a different process.\nandgt;andgt;Renormalization is required because, when standard perturbation theory\nandgt;andgt;is used, it is found that the photon has a divergent mass.
	www.physicsforums.com /showthread.php?t=65552 (5223 words)

	STATISTICAL PHYSICS
		Several of these are classics in the field, including a suite of six works on self-organized criticality and complexity, a pair on diffusion-limited aggregation, some papers on correlations near critical points, a few of the basic sources on the development of the real-space renormalization group, and several papers on magnetic behavior in a plain geometry.
		Kadanoff's pioneering contributions to phase transitions and the renormalization group are covered in a marvellous retrospective that will be engaging to novice and expert alike.
		Scaling theory and renormalization group are described in a remarkably simple and lucid manner.
	www.worldscibooks.com /physics/4016.html (848 words)

	Renormalization: Our Greatly Misunderstood Friend (Site not responding. Last check: 2007-10-10)
		This is a web-paper write-up for a talk I gave for Intermediate Seminar at Johns Hopkins Unversity (172.711-712).
		The ``Algorithm of Renormalization'' will then be presented and explored.
		The Intermediate Seminar at Johns Hopkins University's Physics and Astronomy Deptartment is a year long seminar taken by all second-year graduate students.
	www.pha.jhu.edu /~blechman/papers/renormalization (219 words)

	The search for a Quantum Field Theory
		Since the renormalization group can be derived from elementary quantum field theory only through mathematically meaningless infinite subtractions, one may infer that it cannot therefore be derived from elementary quantum field theory at all.
		A feature of the renormalization group is that the coupling constant of a theory is not in fact a constant at all, and there is a situation where it can go to zero if the momentum transfer is large.
		But let me be clear about renormalization: particle physicists have only got away with this because they have convinced the rest of the scientific community that they are smarter than them.
	www.cgoakley.demon.co.uk /qft (6043 words)

	Renormalization by Fuzzyfication
		And, so the process of the renormalization could be made, you could calculate everything in terms of the experimental mass and then take the limit and the apparent difficulty that the unitary is violated temporarily seems to disappear.
		The core activity of renormalization is the calculation of a convolution integral with a shape function as a kernel.
		Simplified renormalizations can only be substituted iff it has been firmly established that the original functions indeed get lost of their singularities with (the model of) some measurement.
	hdebruijn.soo.dto.tudelft.nl /QED (4727 words)

	Algorithm of Renormalization (Site not responding. Last check: 2007-10-10)
		We have seen what renormalization is in the context of perturbation theory, and we have seen how without renormalization, even the simplest processes in QED would blow up.
		Now we must discuss renormalization itself - how is it accomplished, and how should it be interpreted.
		The first step is to perform the integration and separate out the divergent pieces, and the second step is to get rid of these divergences.
	www.pha.jhu.edu /~blechman/papers/renormalization/node3.html (152 words)

	Renormalization Conditions
		However, in equation (12.30) of chapter 12, he introduces a different set of renormalization conditions defined at a spacelike momentum.
		In Peskin chapter 10, he renormalizes phi^4 theory using the renormalization conditions in equation (10.19), which basically say that the propagator has a pole at p^2 = m^2 and that the 4-point interaction is exact for s=4m^2, t=u=0.
		Now, when first discussing renormalization and for certain elementary physical applications, it is often desirable to parameterize the theory in terms of physically measured variables.
	www.physicsforums.com /showthread.php?p=1064263#post1064263 (1060 words)

	WAVELETS AND RENORMALIZATION
		The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points.
		The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion — i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven.
		The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions — themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context.
	www.worldscibooks.com /mathematics/3066.html (322 words)

	Activity on Wilson Renormalization Group
		In particular, in perturbation theory it is possible to solve the so-called fine-tuning equations which say how to fix the ultraviolet non-invariant action in terms of renormalized parameters in such a way than the physical action becomes consistent with the gauge-symmetry (i.e.
		In this paper we introduced a general scheme to generate an improved (resummed) perturbative solution of the ERGE and we applied it to QCD.
		To elucidate this problem we studied in detail the case of abelian gauge theories in the (unpublished) paper [BS] Wilson renormalization group and improved perturbation theory, M. Bonini, M. Simionato, UPRF-97-05, hep-th/9705146, 24pp.
	www.phyast.pitt.edu /~micheles/curriculum/node7.html (855 words)

	Renormalization (Site not responding. Last check: 2007-10-10)
		n theoretical particle physics, where the idea originated, renormalization was a mathematical recipe to get rid of the cufoff necessary to keep certain quantities finite.
		The process of renormalization corresponds to increasing the effective legnth scale through coarse-graining.
		Explicit illustration may be found in K. Halpern and K. Huang, "Nontrivial directions for scalar fields," Phys.
	web.mit.edu /people/kerson/renormal.htm (267 words)

	Regularization and Renormalization (Site not responding. Last check: 2007-10-10)
		Generally, there's just a single pole left in the final expression for the integral to represent the whole infinity in the integral, and renormalization lets us get rid of that.
		In fact, the terms that we ``forgot'' are purely arbitrary, so we can get rid of anything that we want from the formula for the integral, so we have to choose a ``renormalization scheme,'' sort of like choosing a gauge in electrodynamics (but not really; I'll talk about that below).
		I also studied a bunch of other subjects, and I want to include a bibliography, too, so I'll be sure to add all that in a bit.
	int.phys.washington.edu /REU/1997/student/frey/qfield/node3.html (365 words)

	RENORMALIZATION METHOD
		When the transmitting antenna is below the rooftop, the essential features of a building layout is assumed to be captured by a two-dimensional simulation (which is equivalent to a line source and infinitely high buildings).
		But some kind of renormalization must be taken into account when considering the propagation of a point source in a three-dimensional space.
		One could think of the shortest distance which bypass the obstacles; indeed, for the renormalization of our simulations (presented in section 5) we have used the so-called Manhattan distance which is the shortest distance following the lattice edges representing the discretized layout.
	cuiwww.unige.ch /~luthi/tlm/lbe/node8.html (291 words)

	ELibM Book Review: Fermionic functional integrals and the renormalization group
		These constructions are in general rather complicated because almost all models involve bosonic fields which require a combination of cluster expansions and large-field bounds in addition to renormalization.
		The methods of constructive field theory, in particular the mathematical renormalization group (RG) method are well suited to treating this problem.
		The renormalization group transformation is introduced to deal with singular covariances which are characteristic of physically interesting problems.
	www.emis.de /misc/articles/FKT (2102 words)

	Renormalization - Wikipedia, the free encyclopedia
		Beginning in the 1970s, however, inspired by work on the renormalization group and effective field theory, and despite the fact that Dirac, Feynman and various others -- all of whom belonged to the older generation -- never withdrew their criticisms, attitudes began to change, especially among younger theorists.
		Rivasseau, Vincent ; An introduction to renormalization, Poincaré Seminar (Paris, Oct. 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.) ; Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003) [ISBN 3-7643-0579-7].
		Zinn Justin, Jean ; Phase Transitions and Renormalization Group: from Theory to Numbers, Poincaré Seminar (Paris, Oct. 12, 2002), published in : Duplantier, Bertrand; Rivasseau, Vincent (Eds.) ; Poincaré Seminar 2002, Progress in Mathematical Physics 30, Birkhäuser (2003) [ISBN 3-7643-0579-7].
	en.wikipedia.org /wiki/Renormalization (3777 words)

	Renormalization Group (Site not responding. Last check: 2007-10-10)
		The geometric scaling and universality can both be understood from the "renormalization group theory" developed by Feigenbaum.
		A more complete discussion needs more mathematical symbols than can be used with standard HTML: you can view it only if you download the IBM TechExplorer (sorry, Windows 95 or NT only!).
		It is a remarkable result that these abstract mathematical constructions lead to numbers that can be measured in actual experiments on chaotic fluid and other systems.
	www.cmp.caltech.edu /~mcc/chaos_new/Map_docs/rg.html (296 words)

	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)
		Zinn-Justin J., Renormalization and stochastic quantization, Nuclear Phys.
		Gaite J., Stochastic formulation of the renormalization group: supersymmetric structure and the topology of the space of couplings, J.
	www.emis.de /journals/SIGMA/2006/Paper046 (498 words)

	renormalization
		I want to explain to you the basic idea of renormalization in quantum field theory, and I want to say a bit about how it's related to statistical mechanics.
		It's fun to imagine turning a dial to adjust the distance scale D' and watching the physical coupling constants C' move around like a little dot in n-dimensional space, where n is the number of coupling constants.
		If we assume the gravitational constant is reasonably large near the Planck scale, and we follow the renormalization group flow, we find that it's very small at macroscopic distance scales.
	math.ucr.edu /home/baez/renormalization.html (4102 words)

	Amazon.com: Renormalization Group (Physics Notes): Books: Giuseppe Benfatto,Giovanni Gallavotti (Site not responding. Last check: 2007-10-10)
		Scaling and Renormalization in Statistical Physics (Cambridge Lecture Notes in Physics) by John Cardy
		The notion of renormalization group is not well defined.
		renormalization boxes, beta functional, ultraviolet problem, infrared problem, running couplings, multiscale decomposition, nontrivial fixed point, renormalization transformation, free propagator, liquid problem, anomalous dimension, tree vertex, renormalization theory, renormalization group methods, renormalization group approach, relevant operators, asymptotic freedom, power counting, external lines
	www.amazon.com /Renormalization-Group-Physics-Giuseppe-Benfatto/dp/0691044465 (901 words)

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