Perturbation theory at high energy

1967 ◽  
Vol 52 (1) ◽  
pp. 210-223
Author(s):  
L. M. Brown ◽  
Ik-Ju Kang
Keyword(s):  
Perturbation Theory ◽  
High Energy

EVOLUTION OF CONFORMAL COLOR DIPOLES AND HIGH-ENERGY AMPLITUDES IN $\mathcal{N} = 4$ SYM

2011 ◽  
Vol 04 ◽  
pp. 9-19
Author(s):  
IAN BALITSKY
Keyword(s):  
Perturbation Theory ◽  
Wilson Line ◽  
Energy Operator ◽  
High Energy ◽  
Conformal Structure ◽  
Coefficient Function ◽  
Large N ◽  
Energy Behavior ◽  
Regge Limit ◽  
Point Amplitude

The high-energy behavior of the [Formula: see text] SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large Nc, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the first two orders in coupling constant: BFKL intercept and NLO BFKL intercept calculated in Ref. [1]. As an example of using the Wilson-line OPE, we calculate the coefficient function in front of the pomeron for the correlator of four Z2 currents in the first two orders in perturbation theory.

Perturbation theory for dynamical diffraction calculations

1989 ◽  
Vol 47 ◽  
pp. 482-483
Author(s):  
D.J. Eaglesham
Keyword(s):  
Perturbation Theory ◽  
Systematic Errors ◽  
High Energy ◽  
Bloch Wave ◽  
Dynamical Diffraction ◽  
Crystal Potential ◽  
High Energy Electrons ◽  
Electron Wavefunction ◽  
Fair Degree

The dynamical diffraction of high-energy electrons may be calculated to a fair degree of accuracy by several methods. The most widespread techniques involve either multislice calculations or Bloch wave diagonalisation, the two giving equivalent results for diffracted beam intensities for a given set of conditions. However, both types of calculation are approximate, in that they involve a truncated expansion (of not only the electron wavefunction but also the crystal potential) in the number of diffracting beams. Bloch wave diagonalisations, for example, involve computation times which increase as the cube of the number of beams included in the calculation, so that truncation of the calculation with the smallest possible number of beams is essential. Unfortunately, dynamical diffraction calculations (using either multislice or diagonalisation) tend to converge extremely slowly with increasing number of beams, so that Bloch wave calculations in particular can be highly time-consuming. In addition, it is generally difficult to estimate the magnitude of the systematic errors that truncation has produced. However, the scattering to the outermost beams is generally weak, suggesting that these higher coefficients of the potential may be treated within perturbation theory. The pupose of this paper is to present the equations for a perturbation treatment of truncation.

High-Energy Inelastic Scattering of Electrons in Perturbation Theory

1969 ◽  
Vol 185 (5) ◽  
pp. 1748-1753 ◽  
Author(s):  
R. Jackiw ◽  
G. Preparata
Keyword(s):  
Perturbation Theory ◽  
Inelastic Scattering ◽  
High Energy
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