Renormalization-group equation for high-energy wide-angle scattering inφ4theory

1975 ◽  
Vol 11 (8) ◽  
pp. 2252-2259 ◽  
Author(s):  
George Tiktopoulos
Keyword(s):  
Renormalization Group ◽  
High Energy ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Wide Angle ◽  
Angle Scattering

scholarly journals Renormalization Group Equation for Tsallis Statistics

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Airton Deppman
Keyword(s):  
Renormalization Group ◽  
High Energy ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Scaling Properties ◽  
Hadronic Physics ◽  
Nonextensive Statistics ◽  
Interesting Approach ◽  
High Energy Collisions ◽  
The Many

The nonextensive statistics proposed by Tsallis has found wide applicability, being present even in the description of experimental data from high energy collisions. A system with a fractal structure in its energy-momentum space, named thermofractal, was shown to be described thermodynamically by the nonextensive statistics. Due to the many common features between thermofractals and Hagedorn’s fireballs, this system offers the possibility of investigating the origins of nonextensivity in hadronic physics and in QCD. In this regard, the investigation of the scaling properties of thermofractals through the renormalization group equation, known as Callan–Symanzik equation, can be an interesting approach.

scholarly journals Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

2009 ◽  
Vol 324 (2) ◽  
pp. 414-469 ◽  
Author(s):  
Alessandro Codello ◽  
Roberto Percacci ◽  
Christoph Rahmede
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

High-Energy Small- and Wide-Angle X-Ray Scattering: A Versatile Tool for Materials Analysis

2004 ◽  
Author(s):  
Jonathan Almer
Keyword(s):  
High Energy ◽  
Real Space ◽  
Wide Angle ◽  
X Ray ◽  
Study Materials ◽  
X Ray Scattering ◽  
Angle Scattering ◽  
Wide Range ◽  
Versatile Tool ◽  
Ray Scattering

Acquisition of microstructural information during realistic service conditions is an ongoing need for fundamental materials insight and computational input. In addition, for engineering applications it is often important to be able to study materials over a wide range of penetration depths, from the surface to bulk. In this presentation we discuss developments at the Sector 1-ID beamline of the Advanced Photon Source (APS) to utilize high-energy x-ray scattering for such studies. The use of high-energies (~80 keV) provides a highly penetrating probe, with sampling depths up to several mm in most materials. Through the development and use of high-energy optics, we can perform both small- and wide-angle scattering (SAXS/WAXS), to probe a large range of sample dimensions in reciprocal space (ranging from Angstroms to hundreds of nanometers), with real space resolutions ranging from microns to mm.

scholarly journals LOOP VARIABLES IN STRING THEORY

2003 ◽  
Vol 18 (05) ◽  
pp. 767-809 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Equations Of Motion ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
World Sheet ◽  
Gauge Invariant ◽  
Variable Approach ◽  
Exact Renormalization Group

The loop variable approach is a proposal for a gauge-invariant generalization of the sigma-model renormalization group method of obtaining equations of motion in string theory. The basic guiding principle is space–time gauge invariance rather than world sheet properties. In essence it is a version of Wilson's exact renormalization group equation for the world sheet theory. It involves all the massive modes and is defined with a finite world sheet cutoff, which allows one to go off the mass-shell. On shell the tree amplitudes of string theory are reproduced. The equations are gauge-invariant off shell also. This paper is a self-contained discussion of the loop variable approach as well as its connection with the Wilsonian RG.

Sign in / Sign up

Export Citation Format

Share Document