scholarly journals SOME COMMENTS ON THE DIVERGENCE OF PERTURBATION SERIES IN QUANTUM ELECTRODYNAMICS

2006 ◽  
Vol 21 (14) ◽  
pp. 1161-1166
Author(s):  
MOFAZZAL AZAM
Keyword(s):  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Perturbation Series ◽  
Coupling Constant

It has been argued by Dyson that the perturbation theory in coupling constant in QED cannot be convergent. We find that similar albeit slightly different arguments lead to the divergence of the series of 1/N f expansion in QED.

scholarly journals Singular structure of the QED effective action

2019 ◽  
Vol 49 ◽  
pp. 1960006
Author(s):  
B. A. Fayzullaev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Singular Perturbation ◽  
Effective Action ◽  
Electromagnetic Interaction ◽  
Perturbation Series ◽  
Singular Perturbation Theory ◽  
Quantum Field ◽  
Coupling Constant

The equations for the QED effective action derived in Ref. 3 are considered using singular perturbation theory. The effective action is divided into regular and singular (in coupling constant) parts. It is shown that expression for the regular part coincides with usual Feynman perturbation series over coupling constant, while the remainder has essential singularity at the vanishing coupling constant: [Formula: see text]. This means that in the frame of quantum field theory it is impossible “to switch off” electromagnetic interaction in general and pass on to “free electron”.

scholarly journals A RIGOROUS TREATMENT OF THE PERTURBATION THEORY FOR MANY-ELECTRON SYSTEMS

2009 ◽  
Vol 21 (08) ◽  
pp. 981-1044 ◽  
Author(s):  
YOHEI KASHIMA
Keyword(s):  
Perturbation Theory ◽  
Correlation Functions ◽  
Perturbation Series ◽  
Periodic Lattice ◽  
Electron Systems ◽  
Coupling Constant ◽  
Finite Dimensional ◽  
Higher Order Terms ◽  
Point Correlation ◽  
Rigorous Treatment

Four point correlation functions for many electrons at finite temperature in periodic lattice of dimension d (≥1) are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite dimensional Grassmann integrals. A lower bound on the radius of convergence and an upper bound on the perturbation series are obtained by evaluating the Taylor expansion of logarithm of the finite dimensional Grassmann Gaussian integrals. The perturbation series up to second-order is numerically implemented along with the volume-independent upper bounds on the sum of the higher order terms in the 2-dimensional case.

Energy, Information, and Superluminal Speed in Quantum Electrodynamics

2020 ◽  
pp. 27-33
Author(s):  
Boris A. Veklenko
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Quantum Electrodynamics ◽  
Excited Atom ◽  
Standard Quantum ◽  
Energy Information

Without using the perturbation theory, the article demonstrates a possibility of superluminal information-carrying signals in standard quantum electrodynamics using the example of scattering of quantum electromagnetic field by an excited atom.

scholarly journals Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

2017 ◽  
Vol 32 (27) ◽  
pp. 1750165 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Physical Model ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Point Of View ◽  
Inductive Method ◽  
S Matrix ◽  
Causal Approach

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

scholarly journals Energy spectra of muonic atoms in quantum electrodynamics

2019 ◽  
Vol 204 ◽  
pp. 05007 ◽  
Author(s):  
A. E. Dorokhov ◽  
A. A. Krutov ◽  
A. P. Martynenko ◽  
F. A. Martynenko ◽  
O. S. Sukhorukova
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Energy Spectrum ◽  
Hyperfine Structure ◽  
Nuclear Structure ◽  
Quantum Electrodynamics ◽  
Vacuum Polarization ◽  
Energy Spectra ◽  
Hyperfine Splittings ◽  
S States

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

scholarly journals A strongly perturbed quantum system is a semiclassical system

2007 ◽  
Vol 463 (2085) ◽  
pp. 2195-2200 ◽  
Author(s):  
Marco Frasca
Keyword(s):  
Perturbation Theory ◽  
Quantum System ◽  
Perturbation Series ◽  
Duality Principle

We show that a strongly perturbed quantum system, being a semiclassical system characterized by the Wigner–Kirkwood expansion for the propagator, has the same expansion for the eigenvalues as for the Wentzel–Kramers–Brillouin series. The perturbation series is rederived by the duality principle in perturbation theory.

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