Derivation of the external field in the Dirac equation based on quantum electrodynamics

1983 ◽  
Vol 61 (1) ◽  
pp. 85-92 ◽  
Author(s):  
A. R. Neghabian ◽  
W. Glöckle
Keyword(s):  
Dirac Equation ◽  
External Field ◽  
Quantum Electrodynamics ◽  
Heavy Particle ◽  
External Potential ◽  
Radiative Corrections ◽  
The Individual

The multiphoton exchange between two charged spin [Formula: see text] particles of light (m) and heavy (M) mass is considered and it is shown how, in the limit M → ∞, the Dirac equation with an external potential including radiative corrections emerges. This result can only be achieved if diagrams with photons attached to the heavy particle line cancel among themselves for M → ∞. We have shown this in the lowest order where the individual diagrams have nonvanishing limits.

Null-plane quantum electrodynamics in an external radiation field

1976 ◽  
Vol 54 (22) ◽  
pp. 2246-2271 ◽  
Author(s):  
R. A. Neville
Keyword(s):  
Dirac Equation ◽  
Laser Pulse ◽  
External Field ◽  
Perturbation Method ◽  
Quantum Electrodynamics ◽  
Laser Field ◽  
Field Operator ◽  
External Radiation ◽  
Null Plane ◽  
Electron Field

The formalism developed in this paper is designed to treat the interaction of an electron with a laser pulse. Precisely, it is a formulation on null hyperplanes of quantum electrodynamics in an external radiation field.The result is a quantum electrodynamic formulation in which one works in the Furry picture. The electron field operator in this picture is a solution to the Dirac equation with external field, and is appropriately represented by an expansion in terms of wave packets of Volkov solutions, the latter being exact, explicitly known solutions to the above named equation. The null-plane formulation is required for the consistent construction and implementation of the Volkov wave packets.This formalism permits one to do calculations which take the external field (laser field) into account exactly while treating the quantized photon field (self-field) via the usual perturbation method as adapted to null planes.

scholarly journals Fermions in the Rindler spacetime

2019 ◽  
Vol 16 (09) ◽  
pp. 1950140 ◽  
Author(s):  
L. C. N. Santos ◽  
C. C. Barros
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Reference Frame ◽  
Bound States ◽  
Liouville Problem ◽  
External Potential ◽  
Compact Expression ◽  
Sturm Liouville

In this paper, we study the Dirac equation in the Rindler spacetime. The solution of the wave equation in an accelerated reference frame is obtained. The differential equation associated to this wave equation is mapped into a Sturm–Liouville problem of a Schrödinger-like equation. We derive a compact expression for the energy spectrum associated with the Dirac equation in an accelerated reference. It is shown that the noninertial effect of the accelerated reference frame mimics an external potential in the Dirac equation and, moreover, allows the formation of bound states.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

Radiative Corrections for Electron Scattering in an External Field—A New Method of Calculation

1972 ◽  
Vol 5 (2) ◽  
pp. 358-376 ◽  
Author(s):  
Lester L. DeRaad ◽  
Richard J. Ivanetich ◽  
Kimball A. Milton ◽  
Wu-yang Tsai
Keyword(s):  
External Field ◽  
Electron Scattering ◽  
New Method ◽  
Radiative Corrections ◽  
Method Of Calculation

On renormalization and the ? operation for quantum electrodynamics in an external field

1978 ◽  
Vol 34 (2) ◽  
pp. 98-105
Author(s):  
M. A. Braun ◽  
A. N. Vasil'ev ◽  
A. L. Kitanin ◽  
Yu. M. Pis'mak
Keyword(s):  
External Field ◽  
Quantum Electrodynamics
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