An approximate connection between the oscillator basis “Sussex matrix elements” and the corresponding on- and off-the-energy shell plane wave matrix elements

1969 ◽  
Vol 29 (5) ◽  
pp. 282-284 ◽  
Author(s):  
H.A. Mavromatis ◽  
B. Singh
Keyword(s):  
Plane Wave ◽  
Matrix Elements ◽  
Energy Shell ◽  
Oscillator Basis

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).

CLOSED ANALYTIC FORM FOR EVALUATION OF RELATIVISTIC BOUND-UNBOUND AND UNBOUND-UNBOUND TRANSITION MATRIX ELEMENTS OF HYDROGENIC ATOMS

2008 ◽  
Vol 22 (29) ◽  
pp. 5095-5102
Author(s):  
A. V. SOLDATOV ◽  
J. SEKE ◽  
G. ADAM ◽  
M. POLAK
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Vector Potential ◽  
Transition Matrix ◽  
Analytic Form ◽  
Field Vector ◽  
Matrix Elements ◽  
Plane Wave Expansion ◽  
Transition Matrix Elements ◽  
Closed Analytic Form

A closed analytic form for relativistic bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential is derived. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically.

EVALUATION OF RELATIVISTIC TRANSITION MATRIX ELEMENTS OF HYDROGENIC ATOMS USING PLANE WAVE EXPANSION

2007 ◽  
Vol 21 (22) ◽  
pp. 3825-3840 ◽  
Author(s):  
A. V. SOLDATOV ◽  
J. SEKE ◽  
G. ADAM
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Vector Potential ◽  
Transition Matrix ◽  
Field Vector ◽  
Matrix Elements ◽  
Plane Wave Expansion ◽  
Wave Expansion ◽  
Transition Matrix Elements ◽  
First Time

For the first time to our knowledge, a general, explicit formula for exact transition matrix elements in relativistic hydrogenic atoms is derived, by using the plane-wave expansion for the electromagnetic-field vector potential. By applying the obtained formula, discrete-discrete and discrete-continuous matrix elements are evaluated analytically and numerically.

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