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 On the self-energies and cross-sections of orthodox quantum mechanics

1949 ◽  
Vol 197 (1048) ◽  
pp. 73-89 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Cross Sections ◽  
Negative Energy ◽  
The Self ◽  
Convergence Properties ◽  
Self Energy ◽  
Negative Expectation ◽  
Systematic Development ◽  
Theory Of Fields

In this paper are introduced several novel techniques having as their objects, first, the gain of a new understanding of the divergence difficulties of orthodox quantum theory, and secondly, the systematic development of the quantum mechanics of fields in terms of the density matrix. There is included a new presentation of a form of perturbation theory which has the outstanding advantages over the usual one that it is much more quickly convergent, and leaves the density matrix normalized at every stage so that the diagonal elements representing occupational probabilities cannot diverge. Exact general formulae are derived for self-energies and cross-sections for the purpose of examining their convergence properties. The general theory of fields is developed ab initio , and it is shown that the use of the density matrix in place of the wave vector illuminates and simplifies the customary theory. The second quantization of the density matrix which follows throws unexpected light on the existence of particles with negative expectation values. Finally, the whole theory is applied to the crucial example of the electron or positron in an electromagnetic field. It is confirmed that the self-energy of the electron in the orthodox theory cannot be made finite without the introduction of negative energy photons.

SINGULAR FERMI SURFACES II: THE TWO-DIMENSIONAL CASE

2008 ◽  
Vol 20 (03) ◽  
pp. 275-334 ◽  
Author(s):  
JOEL FELDMAN ◽  
MANFRED SALMHOFER
Keyword(s):  
Perturbation Theory ◽  
Spatial Dimension ◽  
Physical Significance ◽  
The Self ◽  
Two Dimensional ◽  
Singular Case ◽  
Fermi Surfaces ◽  
Self Energy ◽  
Fermion Systems ◽  
Derivatives Of

We consider many-fermion systems with singular Fermi surfaces, which contain Van Hove points where the gradient of the band function k ↦ e(k) vanishes. In a previous paper, we have treated the case of spatial dimension d ≥ 3. In this paper, we focus on the more singular case d = 2 and establish properties of the fermionic self-energy to all orders in perturbation theory. We show that there is an asymmetry between the spatial and frequency derivatives of the self-energy. The derivative with respect to the Matsubara frequency diverges at the Van Hove points, but, surprisingly, the self-energy is C1 in the spatial momentum to all orders in perturbation theory, provided the Fermi surface is curved away from the Van Hove points. In a prototypical example, the second spatial derivative behaves similarly to the first frequency derivative. We discuss the physical significance of these findings.

scholarly journals SINGULAR FERMI SURFACES I: GENERAL POWER COUNTING AND HIGHER DIMENSIONAL CASES

2008 ◽  
Vol 20 (03) ◽  
pp. 233-274 ◽  
Author(s):  
JOEL FELDMAN ◽  
MANFRED SALMHOFER
Keyword(s):  
Perturbation Theory ◽  
Fermi Surface ◽  
Companion Paper ◽  
The Self ◽  
Stat Phys ◽  
Fermi Velocity ◽  
Fermi Surfaces ◽  
Self Energy ◽  
Regularity Properties ◽  
Spatial Dimensions

We prove regularity properties of the self-energy, to all orders in perturbation theory, for systems with singular Fermi surfaces which contain Van Hove points where the gradient of the dispersion relation vanishes. In this paper, we show for spatial dimensions d ≥ 3 that despite the Van Hove singularity, the overlapping loop bounds we proved together with E. Trubowitz for regular non-nested Fermi surfaces [J. Stat. Phys.84 (1996) 1209–1336] still hold, provided that the Fermi surface satisfies a no-nesting condition. This implies that for a fixed interacting Fermi surface, the self-energy is a continuously differentiable function of frequency and momentum, so that the quasiparticle weight and the Fermi velocity remain close to their values in the noninteracting system to all orders in perturbation theory. In a companion paper, we treat the more singular two-dimensional case.

An INDO MO Study on the Ground State and the Cationic States of Cyclopentadienyl Nickel Nitrosyl

1981 ◽  
Vol 36 (12) ◽  
pp. 1361-1366 ◽  
Author(s):  
Michael C. Böhm
Keyword(s):  
Perturbation Theory ◽  
Electronic Structure ◽  
Ground State ◽  
The Self ◽  
Many Body ◽  
Self Energy ◽  
Cyclopentadienyl Ligand ◽  
Energy Part ◽  
Correct Sequence ◽  
Many Body Perturbation Theory

The electronic structure of cyclopentadienyl nickel nitrosyl (1) in the ground state as well as the cationic states of 1 are investigated by means of a semiempirical INDO Hamiltonian and many body perturbation theory. It is demonstrated that the nature of the NiNO coupling is largely covalent while the interaction between the 3d center and the cyclopentadienyl ligand is predominantly of ionic type. The ground state MO sequence of the Ni 3d orbitals is 4e2(3dx²-y²/3dxy) below 7e1(3dXz/3dyz) and 15a1(3dz2). The sequence of the ionization potentials is 8e1 (Cp - π) < 15a1<4e2<7e1. The ionization energies have been determined by means of the Green’s function formalism; the self-energy part has been calculated by a second order and a renormalized approximation. Both procedures predict the correct sequence of ionization events.

Shock Waves and Solitary Waves in Elastic Circular Rod

2011 ◽  
Vol 183-185 ◽  
pp. 2197-2201 ◽  
Author(s):  
Zhi Fang Liu ◽  
Yuan Yuan He ◽  
Shan Yuan Zhang
Keyword(s):  
Wave Equation ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Necessary Condition ◽  
Variation Principle ◽  
Poisson Effect

A nonlinear waves equation of an elastic circular rod taking account of finite deformation and transverse Poisson effect is derived by means of Hamilton variation principle in this paper. Nonlinear wave equation and corresponding truncated nonlinear wave equation are solved by the hyperbolic tangent function and cotangent function finite expansion method. Two different types of exact traveling wave solutions, the shock wave solution and the solitary wave solution are obtained. The necessary condition of these solutions existence is given also.

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