The Zeta Function in Quantum Electrodynamics (QED)

2021 ◽  
pp. 57-68
Author(s):  
Walter Dittrich
Keyword(s):  
Zeta Function ◽  
Quantum Electrodynamics

A simple series representation for Apéry's constant

2013 ◽  
Vol 97 (540) ◽  
pp. 455-460 ◽  
Author(s):  
John Melville
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Quantum Electrodynamics ◽  
Series Representation ◽  
Gyromagnetic Ratio ◽  
French Mathematician ◽  
Series Representations ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Image Position

Apéry's constant is the value of ζ (3) where ζ is the Riemann zeta function. ThusThis constant arises in certain mathematical and physical contexts (in physics for example ζ (3) arises naturally in the computation of the electron's gyromagnetic ratio using quantum electrodynamics) and has attracted a great deal of interest, not least the fact that it was proved to be irrational by the French mathematician Roger é and named after him. See [1,2].Numerous series representations have been obtained for ζ (3) many of which are rather complicated [3]. é used one such series in his irrationality proof. It is not known whether ζ (3) is transcendental, a question whose resolution might be helped by a study of an appropriate series representation of ζ (3).

scholarly journals The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 79 ◽  
Author(s):  
Walter Dittrich
Keyword(s):  
Electromagnetic Field ◽  
Zeta Function ◽  
Quantum Electrodynamics ◽  
External Electromagnetic Field ◽  
Riemann’S Zeta Function ◽  
Mathematics And Physics ◽  
Theory Of Numbers

In particular, Riemann’s impact on mathematics and physics alike is demonstrated using methods originating from the theory of numbers and from quantum electrodynamics, i.e., from the behavior of an electron in a prescribed external electromagnetic field. More specifically, we employ Riemann’s zeta function to regularize the otherwise infinite results of the so-called Heisenberg–Euler Lagrangian. As a spin-off, we also calculate some integrals that are useful in mathematics and physics.

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.

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