Renormalization group and operator product expansion in turbulence: Shell models

1993 ◽  
Vol 48 (3) ◽  
pp. 1823-1838 ◽  
Author(s):  
Gregory L. Eyink
Keyword(s):  
Renormalization Group ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Shell Models

scholarly journals SHORT DISTANCE REPULSION AMONG BARYONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1330012 ◽  
Author(s):  
SINYA AOKI ◽  
JANOS BALOG ◽  
TAKUMI DOI ◽  
TAKASHI INOUE ◽  
PETER WEISZ
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Lattice Qcd ◽  
Operator Product Expansion ◽  
Short Distance ◽  
Numerical Results ◽  
Wave Functions ◽  
Operator Product ◽  
Distance Behavior

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu–Bethe–Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion (OPE) and a renormalization group (RG) analysis in the perturbation theory (PT) of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

scholarly journals Nonperturbative Expansion, Renormalons and τ-Decay

1997 ◽  
Vol 12 (19) ◽  
pp. 1361-1368 ◽  
Author(s):  
H. F. Jones ◽  
A. Ritz ◽  
I. L. Solovtsov
Keyword(s):  
Renormalization Group ◽  
Physical Quantity ◽  
Operator Product Expansion ◽  
Spectral Representation ◽  
Infrared Region ◽  
Operator Product ◽  
Effective Coupling ◽  
Power Corrections

We analyze inclusive τ-decay using a modified version of the a expansion, a nonperturbative technique in which the effective coupling is analytic in the infrared region. The modification involves renormalization group improvement of the integrand in a spectral representation for the D-function prior to implementing the a expansion. The advantage of this approach is that it enables us to monitor the structure of the induced power corrections and to ensure that these are consistent with the operator product expansion. Numerically the method agrees well with experiment: the comparison is made with the physical quantity RZ using Rτ as input.

SYMMETRIES OF THE RENORMALIZATION GROUP EQUATIONS AND THE SCALING LAW REVISITED

1993 ◽  
Vol 08 (32) ◽  
pp. 3017-3023
Author(s):  
P. K. JHA ◽  
K. C. TRIPATHY
Keyword(s):  
Renormalization Group ◽  
Operator Product Expansion ◽  
Scaling Laws ◽  
Scaling Law ◽  
Renormalization Group Equation ◽  
Operator Product ◽  
Electromagnetic Current ◽  
Group Equation ◽  
Infinite Dimensional ◽  
Renormalization Group Equations

The symmetry associated with the renormalization group equation satisfied by the Wilson coefficients in the operator product expansion of the electromagnetic current in deep inelastic scattering is re-examined using Blueman-Cole-Obsiannikov-Olver program. It is shown that the system exhibits infinite-dimensional symmetry. From the characteristics, we derive the detailed solutions of the renormalization group equation and the scaling laws for Wilson moments.

scholarly journals High-energy operator product expansion at sub-eikonal level

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Giovanni Antonio Chirilli
Keyword(s):  
Operator Product Expansion ◽  
Evolution Equations ◽  
Energy Operator ◽  
High Energy ◽  
Structure Functions ◽  
Distribution Functions ◽  
Impact Factors ◽  
Operator Product ◽  
The Impact ◽  
New Distribution

Abstract The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.

scholarly journals Conformal Regge theory at finite boost

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Simon Caron-Huot ◽  
Joshua Sandor
Keyword(s):  
Field Theory ◽  
Operator Product Expansion ◽  
Operator Product ◽  
Exact Results ◽  
Double Integral ◽  
Regge Theory ◽  
Conformal Field ◽  
Regge Trajectories ◽  
Continuous Spins ◽  
Regge Limit

Abstract The Operator Product Expansion is a useful tool to represent correlation functions. In this note we extend Conformal Regge theory to provide an exact OPE representation of Lorenzian four-point correlators in conformal field theory, valid even away from Regge limit. The representation extends convergence of the OPE by rewriting it as a double integral over continuous spins and dimensions, and features a novel “Regge block”. We test the formula in the conformal fishnet theory, where exact results involving nontrivial Regge trajectories are available.

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