scholarly journals THE EXACT RENORMALIZATION GROUP AND APPROXIMATE SOLUTIONS

1994 ◽  
Vol 09 (14) ◽  
pp. 2411-2449 ◽  
Author(s):  
TIM R. MORRIS
Keyword(s):  
Renormalization Group ◽  
Approximation Scheme ◽  
Approximate Solutions ◽  
Flow Equations ◽  
Qualitative And Quantitative ◽  
Nonperturbative Approximation ◽  
Exact Renormalization Group ◽  
Cactus Approximation ◽  
Sharp Cutoff ◽  
The Continuum

We investigate the structure of Polchinski’s formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff Green’s functions are given. A promising nonperturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in “irrelevancy” of operators. We illustrate with two simple models of four-dimensional λφ4 theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.

scholarly journals EXACT RENORMALIZATION GROUP AND MANY-FERMION SYSTEMS

2005 ◽  
Vol 20 (02n03) ◽  
pp. 596-598 ◽  
Author(s):  
B. KRIPPA ◽  
M. C. BIRSE ◽  
J. A. MCGOVERN ◽  
N. R. WALET
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Short Range ◽  
Numerical Solutions ◽  
Scattering Length ◽  
Group Method ◽  
Renormalization Group Method ◽  
Flow Equations ◽  
Fermion Systems ◽  
Exact Renormalization Group

The exact renormalization group method is applied to many-fermion systems with short-range attractive forces. The strength of the attractive fermion-fermion interaction is determined from the vacuum scattering length. A set of approximate flow equations is derived including fermionic bosonic fluctations. The numerical solutions show a phase transition to a gapped phase. The inclusion of bosonic fluctuations is found to be significant only in the small-gap regime.

scholarly journals Renormalization group flow equations with full momentum dependence

2011 ◽  
Vol 369 (1946) ◽  
pp. 2735-2758 ◽  
Author(s):  
Jean-Paul Blaizot
Keyword(s):  
Renormalization Group ◽  
Einstein Condensation ◽  
Momentum Dependence ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Bose Einstein ◽  
Exact Renormalization Group ◽  
Group Flow ◽  
Truncation Of The Hierarchy

After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the n -point functions. Applications are then briefly presented, to critical O ( N ) models, to Bose–Einstein condensation and to finite-temperature field theory.

scholarly journals GAUGE INVARIANT EXACT RENORMALIZATION GROUP AND PERFECT ACTIONS IN THE OPEN BOSONIC STRING THEORY

2007 ◽  
Vol 22 (23) ◽  
pp. 1701-1715 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
Lattice Gauge Theory ◽  
Equations Of Motion ◽  
Finite Lattice ◽  
Open String ◽  
Scale Invariant ◽  
Gauge Invariant ◽  
Lattice Gauge ◽  
Exact Renormalization Group ◽  
The Continuum

The exact renormalization group is applied to the worldsheet theory describing bosonic open string backgrounds to obtain the equations of motion for the fields of the open string. Using loop variable techniques the equations can be constructed to be gauge invariant. Furthermore they are valid off the (free) mass shell. This requires keeping a finite cutoff. Thus we have the interesting situation of a scale invariant worldsheet theory with a finite worldsheet cutoff. This is possible because there is infinite number of operators whose coefficients can be tuned. This is in the same sense that "perfect actions" or "improved actions" have been proposed in lattice gauge theory to reproduce the continuum results even while keeping a finite lattice spacing.

scholarly journals EXACT RENORMALIZATION GROUP EQUATIONS AND THE FIELD THEORETICAL APPROACH TO CRITICAL PHENOMENA

2001 ◽  
Vol 16 (11) ◽  
pp. 1825-1845 ◽  
Author(s):  
C. BAGNULS ◽  
C. BERVILLIER
Keyword(s):  
Renormalization Group ◽  
Critical Phenomena ◽  
Theoretical Approach ◽  
Continuum Limit ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Perturbative Approach ◽  
Renormalization Group Equations ◽  
Exact Renormalization Group ◽  
The Continuum

After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as the continuum limit and the renormalizability and the pressure of singularities in the perturbative series are discussed.

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

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