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.

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 NONCOMMUTATIVE U(1) SUPER-YANG–MILLS THEORY: PERTURBATIVE SELF-ENERGY CORRECTIONS

2004 ◽  
Vol 19 (25) ◽  
pp. 4231-4249 ◽  
Author(s):  
A. A. BICHL ◽  
M. ERTL ◽  
A. GERHOLD ◽  
J. M. GRIMSTRUP ◽  
L. POPP ◽  
...  
Keyword(s):  
Power Counting ◽  
The Self ◽  
Field Theories ◽  
Yang Mills ◽  
Self Energy ◽  
Supersymmetric Field Theories ◽  
Crucial Feature ◽  
The One ◽  
Infrared Divergences ◽  
Super Yang Mills Theory

The quantization of the noncommutative [Formula: see text], U(1) super-Yang–Mills action is performed in the superfield formalism. We calculate the one-loop corrections to the self-energy of the vector superfield. Although the power-counting theorem predicts quadratic ultraviolet and infrared divergences, there are actually only logarithmic UV and IR divergences, which is a crucial feature of noncommutative supersymmetric field theories.

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.

Vacancies in close-packed polyvalent metals

1970 ◽  
Vol 316 (1525) ◽  
pp. 201-222 ◽  
Keyword(s):  
Bloch Wave ◽  
Wave Functions ◽  
The Self ◽  
Radial Wave ◽  
Conduction Electrons ◽  
Self Energy ◽  
Crystal Density ◽  
Self Consistent ◽  
The One ◽  
Formation Energies

The difference in total energy of a crystal with and without a vacancy involves essentially three terms: (i) The change in the one-electron eigenvalues due to scattering of conduction electrons off the vacant site. (ii) The self-energy of the displaced charge. (iii) The change in exchange and correlation energies of the electron gas. We have investigated the contributions (i) to (iii) for Cu, Mg, Al and Pb. The change in the one-electron eigenvalues is shown to be insensitive to the Bloch wave character of the wave functions and also to the choice of the repulsive potential V ( r ) representing the effect of the vacancy on the conduction electrons. There is thus no difficulty in evaluating contribution (i) for metals of different valencies. In contrast, the self-energy of the displaced charge is shown to depend very sensitively on the choice of V ( r ), and it is, therefore, essential to make the calculation self-consistent. This we have done by properly screening the negative of the point ion fields for Cu + to Pb 4+ . The radial wave functions and phase shifts for the low order partial waves have been evaluated, and self-consistent displaced charges obtained. The exchange energy has been estimated from a Dirac–Slater type of approximation and is again not sensitive to the detailed form of the displaced charge, while the change in correlation energy is found to be unimportant in determining the vacancy formation energy. The formation energies for the polyvalent metals are in satisfactory agreement with experiment. Some results for excess resistivities due to vacancies in metals are also presented. Here, in contrast to the calculation of the formation energies, it is essential to account for the Bloch wave character of the electron waves scattered by the vacancy. It is also proposed that the displaced charge round a vacancy may be a useful building block (or pseudoatom) for forming the crystal density.

Coulomb Gauge Quantization and Renormalization of the Chern–Simons Theory Coupled to Fermions

1997 ◽  
Vol 12 (16) ◽  
pp. 2889-2901 ◽  
Author(s):  
M. Fleck ◽  
A. Foerster ◽  
H. O. Girotti ◽  
M. Gomes ◽  
J. R. S. Nascimento ◽  
...  
Keyword(s):  
Coulomb Gauge ◽  
The Self ◽  
Simons Theory ◽  
Fermion Propagator ◽  
Lorentz Covariance ◽  
Self Energy ◽  
The One ◽  
Chern Simons ◽  
Physical Quantities ◽  
Chern Simons Theory

We study the quantization and the one-loop renormalization of the model resulting from the coupling of charged fermions with a Chern–Simons field, in the Coulomb gauge. A proof of the Lorentz covariance of the physical quantities follows after establishing the Dirac–Schwinger algebra for the Poincaré densities and the transformation properties of the fields under the Poincaré group. The Coulomb gauge one-loop renormalization program is, afterwards, implemented. The noncovariant form of the one-loop fermion propagator, Chern–Simons field propagator and the vertex are explicitly obtained. Finally, the electron anomalous magnetic moment is calculated stressing that, due to the peculiarities of the Coulomb gauge, the contributions from the self-energy diagrams turn out to be essential.

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

CONDENSATE FRACTION IN THE DYNAMIC STRUCTURE FUNCTION OF BOSE FLUIDS

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2169-2180
Author(s):  
M. SAARELA ◽  
F. MAZZANTI ◽  
V. APAJA
Keyword(s):  
Structure Function ◽  
Wave Length ◽  
Impulse Approximation ◽  
Dynamic Structure ◽  
Short Wave ◽  
The Self ◽  
Condensate Fraction ◽  
Self Energy ◽  
Short Wave Length ◽  
The One

We present results on the behavior of the dynamic structure function in the short wave length limit using the equation of motion method. The one-body continuity equation defines the self-energy, which becomes a functional of the fluctuating two-body correlation function. We evaluate the self-energy in this limit and show that sum rules up to the second moment, which requires the self-energy in the short wave length limit and zero frequency to be proportional to the kinetic energy per particle, are exactly satisfied. We compare our results with the impulse approximation and calculate the condensate fraction. An analytic expression for the momentum distribution is also derived.

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