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Search Results (4)

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Keywords = Heisenberg-Euler Lagrangian

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17 pages, 277 KiB  
Article
On-Shell Calculation of Low-Energy Photon–Photon Scattering
by Barry R. Holstein
Universe 2025, 11(5), 134; https://doi.org/10.3390/universe11050134 - 24 Apr 2025
Viewed by 300
Abstract
Although photon–photon scattering does not exist at the tree level, this is no longer the case at loop order and was first calculated by Euler and Heisenberg. The existence of this phenomenon has now been confirmed experimentally by the ATLAS collaboration and plays [...] Read more.
Although photon–photon scattering does not exist at the tree level, this is no longer the case at loop order and was first calculated by Euler and Heisenberg. The existence of this phenomenon has now been confirmed experimentally by the ATLAS collaboration and plays a small but important role in the calculation of gμ-2. We show how the low-energy form of the γγ scattering amplitude can be determined via causal (on-shell) methods using Compton scattering helicity amplitudes as input for the case of charged S = 0, S = 1/2, and S = 1 intermediate state fields. Full article
(This article belongs to the Section Field Theory)
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9 pages, 874 KiB  
Article
Penrose Scattering in Quantum Vacuum
by José Tito Mendonça
Photonics 2024, 11(5), 448; https://doi.org/10.3390/photonics11050448 - 10 May 2024
Cited by 1 | Viewed by 5604
Abstract
This paper considers the scattering of a probe laser pulse by an intense light spring in a QED vacuum. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with the scattering of light by a rotating [...] Read more.
This paper considers the scattering of a probe laser pulse by an intense light spring in a QED vacuum. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with the scattering of light by a rotating black hole, which is usually called Penrose superradiance. Here, the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components having slightly different frequencies, the energy profile of the intense laser beam rotates with an angular velocity that depends on the frequency difference. The nonlinear properties of a quantum vacuum are described by a first-order Euler–Heisenberg Lagrangian. It is shown that in such a configuration, nonlinear photon–photon coupling leads to scattered radiation with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favorable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium. Full article
(This article belongs to the Special Issue Extreme Lasers)
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41 pages, 1172 KiB  
Review
On Instabilities Caused by Magnetic Background Fields
by Michael Bordag
Symmetry 2023, 15(6), 1137; https://doi.org/10.3390/sym15061137 - 23 May 2023
Cited by 1 | Viewed by 1541
Abstract
We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due [...] Read more.
We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due to the tachyonic mode, such a state is not stable, and the question about the true ground state of QCD is still open. In the electroweak model, the corresponding instability is postponed to very large background fields and may be of relevance in the early universe, at best. We start with an introduction to the topic and display the necessary formulas and methods. Then, we consider the one-particle spectra of the fields in a magnetic background and the related Euler–Heisenberg Lagrangians. In addition, we discuss the potential instability connected with the anomalous moment of the electron. The main part is on the quantum correction to the energy in non-Abelian fields, including massive ones. Here, the focus is on so-called electroweak magnetism and the search for a classical solution of the field equations and their approximations by a lattice of flux tubes. Finally, we review approaches with non-homogeneous background fields and the background of an A0-field. Full article
(This article belongs to the Special Issue Review on Quantum Field Theory)
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10 pages, 239 KiB  
Article
The Role of Riemann’s Zeta Function in Mathematics and Physics †,‡
by Walter Dittrich
Universe 2019, 5(3), 79; https://doi.org/10.3390/universe5030079 - 14 Mar 2019
Cited by 3 | Viewed by 3778
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Quantum Fields – From Fundamental Concepts to Phenomenological Questions)
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