PQED: 30 Years of Reduced Quantum Electrodynamics

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

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

Title: Pseudo Quantum Electrodynamics: 30 Years of Reduced QED
Authors: E. C. Marino (1), Leandro O. Nascimento (2), Van Sérgio Alves (2), Danilo T. Alves (2)
(1) Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972 Rio de Janeiro, Brazil
(2) Faculdade de Física, Universidade Federal do Pará, 66075-110 Belém, Brazil
Abstract: Charged quasi-particles, which are constrained to move on a plane, interact through electromagnetic (EM) fields that are not subject to this constraint, living, therefore, 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 the U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM  nteraction 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 the latter would produce a ln r potential. In spite of possessing a nonlocal Lagrangean, PQED has been shown to respect 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: the p-electrons of graphene, silicene and transition metal dicalchogenides, systems exhibiting the Valley Quantum Hall Effect, systems inside cavities, bosonization in  2+1D and so on. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics).

Authors: Han-Jie Zhu, Yi-Hui Xing