scholarly journals CONSTRUCTION OF ASYMPTOTIC FIELDS FOR A CHARGED PARTICLE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250133 ◽  
Author(s):  
O. W. GREENBERG ◽  
STEVE COWEN
Keyword(s):  
Charged Particle ◽  
Momentum Space ◽  
Quantum Electrodynamics ◽  
Delta Function ◽  
Matrix Elements ◽  
Massless Particles ◽  
Principal Value ◽  
Asymptotic Fields

Asymptotic fields do not exist in theories with massless particles and fields, because the vacuum matrix elements of products of the interacting fields in such theories do not have delta function or principal value singularities in momentum space. We remedy this problem by constructing a field for the charged particle that does have the required singularities in momentum space. We illustrate this construction in quantum electrodynamics (QED).

scholarly journals Toward massless and massive event shapes in the large-β0 limit

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
N. G. Gracia ◽  
V. Mateu
Keyword(s):  
Top Quark ◽  
Matrix Elements ◽  
Position Space ◽  
Positive Real ◽  
Full Agreement ◽  
Anomalous Dimensions ◽  
Fixed Order ◽  
Principal Value ◽  
Contour Deformation ◽  
Perturbative Corrections

Abstract We present results for SCET and bHQET matching coefficients and jet functions in the large-β0 limit. Our computations exactly predict all terms of the form $$ {\alpha}_s^{n+1}{n}_f^n $$ α s n + 1 n f n for any n ≥ 0, and we find full agreement with the coefficients computed in the full theory up to $$ \mathcal{O}\left({\alpha}_s^4\right) $$ O α s 4 . We obtain all-order closed expressions for the cusp and non-cusp anomalous dimensions (which turn out to be unambiguous) as well as matrix elements (with ambiguities) in this limit, which can be easily expanded to arbitrarily high powers of αs using recursive algorithms to obtain the corresponding fixed-order coefficients. Examining the poles laying on the positive real axis of the Borel-transform variable u we quantify the perturbative convergence of a series and estimate the size of non-perturbative corrections. We find a so far unknown u = 1/2 renormalon in the bHQET hard factor Hm that affects the normalization of the peak differential cross section for boosted top quark pair production. For ambiguous series the so-called Borel sum is defined with the principal value prescription. Furthermore, one can assign an ambiguity based on the arbitrariness of avoiding the poles by contour deformation into the positive or negative imaginary half-plane. Finally, we compute the relation between the pole mass and four low-scale short distance masses in the large-β0 approximation (MSR, RS and two versions of the jet mass), work out their μ- and R-evolution in this limit, and study how their implementation improves the convergence of the position-space bHQET jet function, whose three-loop coefficient in full QCD is numerically estimated.

Rotational excitations of diatomic molecule with delta potential barrier

2018 ◽  
Vol 17 (04) ◽  
pp. 1850022
Author(s):  
Sonia Lumb ◽  
Shalini Lumb ◽  
Vinod Prasad
Keyword(s):  
Diatomic Molecule ◽  
Applied Field ◽  
Morse Potential ◽  
Short Range ◽  
Delta Function ◽  
Energy Spectra ◽  
Matrix Elements ◽  
Delta Potential ◽  
Homonuclear Diatomic Molecule ◽  
Delta Functions

The interatomic interactions in a diatomic molecule can be fairly modeled by the Morse potential. Short range interactions of the molecule with the neighboring environment can be analyzed by modifying this potential by delta functions. Energy spectra and radial matrix elements have been calculated using an accurate nine-point finite-difference method for such an interacting homonuclear diatomic molecule. The effect of the strength and position of a single delta function interaction on the alignment of this molecule has been studied. The dependence of alignment on the strength of applied field has also been analyzed.

scholarly journals Wave-packet propagation in momentum space: Calculation of sharp-energyS-matrix elements

1992 ◽  
Vol 46 (5) ◽  
pp. 2304-2316 ◽  
Author(s):  
Zeki C. Kuruoğlu ◽  
F. S. Levin
Keyword(s):  
Wave Packet ◽  
Momentum Space ◽  
Matrix Elements

Renormalization of the transformation operators of quantum electrodynamics

1954 ◽  
Vol 227 (1168) ◽  
pp. 94-102
Keyword(s):  
Quantum Electrodynamics ◽  
Matrix Theory ◽  
Transformation Operator ◽  
Time Interval ◽  
Matrix Elements ◽  
Finite Time Interval ◽  
Time Intervals ◽  
Starting Point ◽  
The Matrix ◽  
Long Time

The transformation operator of electrodynamics for a finite time interval with uncertain boundaries is represented by a continuous switching on and off of the charge. It is shown that its divergencies are the same as those appearing in the S matrix theory, and a covariant procedure is given for isolating their infinite parts. Provided Gupta’s renormalized Lagrangian is used as a starting point all the infinities may be removed. The coefficients of the counter terms are power series in the time-dependent charge with coefficients that are independent of the time interval being considered. The practice of approximating the matrix elements of the transformation operators for long time intervals by matrix elements of the S matrix is discussed and justified. In an appendix the extension of these results to the renormalizable meson theories is discussed.

scholarly journals A New Family of Interactions between Clothed Particles in QED

2021 ◽  
Vol 66 (10) ◽  
pp. 833
Author(s):  
A. Arslanaliev ◽  
Y. Kostylenko ◽  
O. Shebeko
Keyword(s):  
Perturbation Theory ◽  
Compton Scattering ◽  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
Energy Shell ◽  
New Family ◽  
Shell Matrix ◽  
Electron Positron ◽  
S Matrix ◽  
Novel Interactions

The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

MAXWELL'S EQUATIONS AND MATRIX ELEMENTS IN QUANTUM ELECTRODYNAMICS

1961 ◽  
Vol 39 (1) ◽  
pp. 141-144
Author(s):  
H. A. Venables
Keyword(s):  
Quantum Electrodynamics ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Second Order ◽  
Matrix Elements

Matrix elements of second-order processes in quantum electrodynamics are obtainable directly from the use of Maxwell's and Dirac's equations.

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