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Entropy
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PQED: 30 Years of Reduced Quantum Electrodynamics
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PQED: 30 Years of Reduced Quantum Electrodynamics

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 4423

Special Issue Editors

Prof. Dr. Thors Hans Hansson

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Guest Editor
AlbaNova University Center, Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
Interests: quantum field theory; condensed matter physics; effective field theories; topological states of matter
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Danilo Teixeira Alves

E-Mail Website
Guest Editor
Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil
Interests: quantum field theory applied to 2+1D systems in condensed matter; quantum vacuum effects (Casimir and dynamical Casimir effect)
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Van Sérgio Alves

E-Mail Website
Guest Editor
Faculdade de Física, Universidade Federal do Pará, Belém 66075-110, PA, Brazil
Interests: quantum field theory applied to 2+1D systems in condensed matter; renormalization group theory; graphene
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In condensed matter systems, the kinematics of the relevant charged quasi-particles is often constrained either to a line or to a plane. Polyacetylene and graphene are some of the most studied examples of the former and the latter, respectively. The electromagnetic (EM) field through which such quasi-particles interact, however, remains fully three-dimensional. We have in hands, therefore, a strange theory postulating that the EM field and the particles that interact through it live in different dimensions. The solution for this situation was provided 30 years ago by E. C. Marino [Nucl. Phys. B408 (1993) 551]. Taking quantum electrodynamics (QED) in 3+1D as a starting point, an effective theory was developed, which completely describes the electromagnetic interaction of particles constrained to move on a plane and whose EM field is subject to the same constraint. Such an effective, dimensionally reduced QED was called pseudo-quantum electrodynamics (PQED) (also known as reduced quantum electrodynamics). It was demonstrated that, despite being nonlocal, PQED respects causality and unitary. It has been applied quite successfully to describe the quantum valley Hall effect in graphene, as well as describing the residual resistivity in this material. It was also successfully applied in the determination of the gyromagnetic ratio in graphene. Significant results were also obtained in transition metal dichalcogenides (TMD), where it produced theoretical prediction of exciton energy spectrum and lifetimes in excellent agreement with the experimental data. Several interesting results were also obtained in the description of graphene inside cavities. The proposed Special Issue hereby proposed shall cover most of the technical and phenomenological aspects of PQED. 

Thus, we invite researchers working on subjects related to PQED to submit contributions to this Special Issue. Topics of interest include (but are not limited to) applications of PQED to:

  • Graphene;
  • Transition-metal dichalcogenides (TMDs);
  • Excitons;
  • Valley quantum hall effect;
  • Cavity effects.

You may choose our Joint Special Issue in Condensed Matter.

Prof. Dr. Thors Hans Hansson
Prof. Dr. Danilo Teixeira Alves
Prof. Dr. Van Sérgio Alves
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • pseudo-quantum electrodynamics
  • reduced quantum electrodynamics
  • effective theories
  • 2+1D
  • graphene
  • transition-metal dichalcogenides

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Published Papers (3 papers)

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Research

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14 pages, 307 KiB  
Article
Fried-Yennie Gauge in Pseudo-QED
by Ana Mizher, Alfredo Raya and Khépani Raya
Entropy 2024, 26(2), 157; https://doi.org/10.3390/e26020157 - 11 Feb 2024
Cited by 1 | Viewed by 1269
Abstract
The Fried-Yennie gauge is a covariant gauge for which the mass-shell renormalization procedure can be performed without introducing spurious infrared divergences to the theory. It is usually applied in calculations in regular Quantum Electrodynamics (QED), but it is particularly interesting when employed in [...] Read more.
The Fried-Yennie gauge is a covariant gauge for which the mass-shell renormalization procedure can be performed without introducing spurious infrared divergences to the theory. It is usually applied in calculations in regular Quantum Electrodynamics (QED), but it is particularly interesting when employed in the framework of pseudo-QED (PQED), where fermions are constrained to 2 + 1 dimensions while the dynamical fields interacting with these fermions live in the bulk of a 3 + 1 space. In this context, the gauge parameter can be adjusted to match the power of the external momentum in the denominator of the photon propagator, simplifying the infrared region without the need for a photon mass. In this work, we apply this machinery, for the first time, to PQED, generalizing the procedure to calculate the self energy in arbitrary dimensions, allowing, of course, for different dimensionalities of fermions and gauge fields. Full article
(This article belongs to the Special Issue PQED: 30 Years of Reduced Quantum Electrodynamics)
17 pages, 368 KiB  
Article
Reduced QED with Few Planes and Fermion Gap Generation
by Eduard V. Gorbar, Valery P. Gusynin and Maxim R. Parymuda
Entropy 2023, 25(9), 1317; https://doi.org/10.3390/e25091317 - 9 Sep 2023
Cited by 3 | Viewed by 1196
Abstract
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of a few atomically thick layers, and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to N planes and contains N [...] Read more.
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of a few atomically thick layers, and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced theory describes charged fermions confined to N planes and contains N vector fields with Maxwell’s action modified by non-local form factors whose explicit form is determined. Taking into account the polarization function, the explicit formulae for the screened electromagnetic interaction are presented in the case of two and three layers. For a heterostructure with two atomically thick layers and charged fermions described by the massless Dirac equation, the dynamical gap generation of the excitonic type is studied. It is found that additional screening due to the second layer increases the value of the critical coupling constant for the gap generation compared to that in graphene. Full article
(This article belongs to the Special Issue PQED: 30 Years of Reduced Quantum Electrodynamics)
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Review

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10 pages, 280 KiB  
Review
Pseudo-Quantum Electrodynamics: 30 Years of Reduced QED
by Eduardo C. Marino, Leandro O. Nascimento, Van Sérgio Alves and Danilo T. Alves
Entropy 2024, 26(11), 925; https://doi.org/10.3390/e26110925 - 30 Oct 2024
Cited by 1 | Viewed by 920
Abstract
Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and [...] Read more.
Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct 1/r Coulomb potential between static charges, whereas QED(2 + 1) produces lnr potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics). Full article
(This article belongs to the Special Issue PQED: 30 Years of Reduced Quantum Electrodynamics)
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