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

scholarly journals Existence of ground state of an electron in the BDF approximation

2014 ◽  
Vol 26 (05) ◽  
pp. 1450007 ◽  
Author(s):  
Jérémy Sok
Keyword(s):  
External Field ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Adjoint Operator ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Relativistic Electrons ◽  
Relativistic Limit ◽  
Existence Of Minimizers ◽  
Dirac Sea

The Bogoliubov–Dirac–Fock (BDF) model allows us to describe relativistic electrons interacting with the Dirac sea. It can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons are neglected. This paper treats the case of an electron together with the Dirac sea in the absence of any external field. Such a system is described by its one-body density matrix, an infinite rank, self-adjoint operator. The parameters of the model are the coupling constant α > 0 and the ultraviolet cut-off Λ > 0: we consider the subspace of squared integrable functions made of the functions whose Fourier transform vanishes outside the ball B(0, Λ). We prove the existence of minimizers of the BDF energy under the charge constraint of one electron and no external field provided that α, Λ-1 and α log(Λ) are sufficiently small. The interpretation is the following: in this regime the electron creates a polarization in the Dirac vacuum which allows it to bind. We then study the non-relativistic limit of such a system in which the speed of light tends to infinity (or equivalently α tends to zero) with αlog(Λ) fixed: after rescaling and translation the electronic solution tends to a Choquard–Pekar ground state.

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.

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