Quantum Electrodynamics: The Self-Energy Problem

1950 ◽  
Vol 78 (2) ◽  
pp. 98-103 ◽  
Author(s):  
Hartland S. Snyder
Keyword(s):  
Quantum Electrodynamics ◽  
The Self ◽  
Energy Problem ◽  
Self Energy

scholarly journals AN ANALYSIS OF THE SELF-ENERGY PROBLEM FOR THE ELECTRON IN QUANTUM ELECTRODYNAMICS

1952 ◽  
Vol 30 (1) ◽  
pp. 70-78
Author(s):  
P. N. Daykin
Keyword(s):  
Quantum Electrodynamics ◽  
The Self ◽  
Positive Energy ◽  
Energy Problem ◽  
Electron Theory ◽  
Hole Theory ◽  
Self Energy ◽  
Virtual Photons ◽  
S Matrix ◽  
The One

Feynman's S-matrix for the self-energy of the free resting electron is evaluated without the restriction that the virtual photons in the intermediate state have only positive energy. Both the one-electron theory and the hole theory of the positron are treated. It is shown that in the one-electron theory the normally quadratically divergent transverse part of the self-energy vanishes if the photon field is assumed to be symmetric in positive and negative energies. A similar theorem does not hold in the hole theory. A particular type of interaction leads to a vanishing self-energy in one-electron theory. However, this does not solve the self-energy problem, as in this case radiation corrections to scattering would vanish as well. The S-matrix for the self-energy of a bound electron is evaluated in a similar manner. The decay probability for an excited state is calculated as the imaginary part of the self-energy. The correct value is obtained only in hole theory and in interaction with positive energy photons. In the special case in which the external field is a uniform magnetic field, again only hole theory with this same interaction gives the correct value for the anomalous magnetic moment.

scholarly journals On the electrodynamic self-energy of the electron

1948 ◽  
Vol 195 (1041) ◽  
pp. 163-173
Keyword(s):  
Perturbation Theory ◽  
Wave Equation ◽  
Quantum Electrodynamics ◽  
Energy State ◽  
Energy Eigenvalue ◽  
Expansion Method ◽  
Negative Energy ◽  
The Self ◽  
Variation Principle ◽  
Self Energy

The stationary-state wave equation for an electron at rest in a negative-energy state in interaction with only its own electromagnetic field is considered. Quantum electrodynamics, single-electron theory and a ‘cut-off’ procedure in momentum-space are used. Expressions in the form of expansions in powers of e 2 /hc are derived for the wave function ψ and the energy-eigenvalue E by a method which (unlike perturbation theory) is not based on the assumption that the self-energy is small. The convergence of the expansion for E is not proved rigorously but the first few terms are shown to decrease rapidly. For low cut-off frequencies K 0 the expression for E behaves as the equivalent perturbation expression but for large K 0 it behaves as — J(e 2 /hc) hK0. The variation principle is applied to an approximation (obtained from the expansion method) for r/r, and it is proved rigorously that for large K 0 the self-energy is algebraically less than or equal to —J(e 2 /hc) hK 0 . Hence, if the electron wave-equation is considered as the limiting case of the ‘cut-off’ equation as K 0 ->ao, it is established that the divergences obtained are not merely due to improper use of perturbation theory and that the self-energy is indeed infinite.

ON THE POSSIBLE EXISTENCE OF A DERIVATIVE COUPLING IN QUANTUM ELECTRODYNAMICS

1959 ◽  
Vol 37 (12) ◽  
pp. 1339-1343
Author(s):  
F. A. Kaempffer
Keyword(s):  
Cross Section ◽  
Quantum Electrodynamics ◽  
Mass Difference ◽  
Large Mass ◽  
The Self ◽  
Nucleon Mass ◽  
Muon Scattering ◽  
Derivative Coupling ◽  
Self Energy ◽  
Classical Analogue

Within the framework of quantum electrodynamics there exists the possibility of a derivative coupling between source and photon field, referred to as eΛ-charge, which has no classical analogue. For calculations the usual graph technique can be used, provided the factor eγμ contributed by each vertex in a conventional graph is replaced by ieΛkμ, where Λ is a length characteristic of the new interaction. Using as cutoff the nucleon mass M one finds for a bare source of electronic mass m the self-energy in second order to be Λm/m ≈ 200, if Λ−1 ≈ 60 M. It is argued that the large mass difference between muon and electron may be due to this effect, assuming muon and electron to differ only in that the muon has eΛ-charge whereas the electron has not. An estimate is made of the muon–muon scattering cross section caused by the presence of eΛ-charge on the muon, and it is found that the existence of this derivative coupling may have escaped observation.

scholarly journals A New Attempt on the Self-Energy Problem of the Photon

1952 ◽  
Vol 8 (3) ◽  
pp. 265-279 ◽  
Author(s):  
O. Hara ◽  
H. Shimazu
Keyword(s):  
The Self ◽  
Energy Problem ◽  
Self Energy

scholarly journals Toward high-precision values of the self energy of non-S states in hydrogen and hydrogen-like ions

2005 ◽  
Vol 83 (4) ◽  
pp. 447-454 ◽  
Author(s):  
E -O Le Bigot ◽  
U D Jentschura ◽  
P Indelicato ◽  
P J Mohr
Keyword(s):  
High Precision ◽  
Quantum Electrodynamics ◽  
Energy Levels ◽  
The Self ◽  
Level Shift ◽  
Atomic Systems ◽  
Self Energy ◽  
Rydberg Constant ◽  
Energy Level Shift ◽  
Nuclear Charge Number

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between 20 and 110 are given for a large number of states. The self-energy is the largest contribution of quantum electrodynamics (QED) to the energy levels of these atomic systems. These results greatly expand the number of levels for which the self energy is known with a controlled and high precision. Applications include the adjustment of the Rydberg constant and atomic calculations that take into account QED effects.PACS Nos.: 12.20.Ds, 31.30.Jv, 06.20.Jr, 31.15.–p

scholarly journals Remark on the Self Energy Problem of the Photon

1952 ◽  
Vol 7 (5-6) ◽  
pp. 591-592
Author(s):  
O. Hara ◽  
H. Shimazu
Keyword(s):  
The Self ◽  
Energy Problem ◽  
Self Energy

scholarly journals An Algebraic Description of Perturbation Theory in Quantum Electrodynamics

1982 ◽  
Vol 35 (6) ◽  
pp. 661 ◽  
Author(s):  
JD Wright
Keyword(s):  
Quantum Electrodynamics ◽  
Algebraic Approach ◽  
Vacuum State ◽  
The Self ◽  
Energy Calculation ◽  
Field Algebra ◽  
Self Energy ◽  
Algebraic Description ◽  
Feynman Rules ◽  
Algebraic Formulation

We use an algebraic formulation of the electromagnetic field, in which various quantization procedures can be described, to discuss perturbation calculations. We show that the Feynman rules and the second order calculation of the self-energy of the electron can be developed on the basis of the Fermi method of quantization. The algebraic approach clarifies the problems in defining the vacuum and other states, which are associated with calculations in terms of field algebra operators. We demonstrate that the 'vacuum' state defined on the field algebra by Schwinger leads to incorrect results in the self-energy calculation.

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