Version 1
: Received: 25 April 2024 / Approved: 26 April 2024 / Online: 26 April 2024 (07:55:14 CEST)
How to cite:
Nascimento, L.O.; Junior, C.A.; Santos, J.R. The Effective Potential of Reduced Models in (21)D+. Preprints2024, 2024041706. https://doi.org/10.20944/preprints202404.1706.v1
Nascimento, L.O.; Junior, C.A.; Santos, J.R. The Effective Potential of Reduced Models in (21)D+. Preprints 2024, 2024041706. https://doi.org/10.20944/preprints202404.1706.v1
Nascimento, L.O.; Junior, C.A.; Santos, J.R. The Effective Potential of Reduced Models in (21)D+. Preprints2024, 2024041706. https://doi.org/10.20944/preprints202404.1706.v1
APA Style
Nascimento, L.O., Junior, C.A., & Santos, J.R. (2024). The Effective Potential of Reduced Models in (21)D+. Preprints. https://doi.org/10.20944/preprints202404.1706.v1
Chicago/Turabian Style
Nascimento, L.O., Carlos A.P.C. Junior and José R. Santos. 2024 "The Effective Potential of Reduced Models in (21)D+" Preprints. https://doi.org/10.20944/preprints202404.1706.v1
Abstract
The description of the electron-electron interactions in two-dimensional materials has a dimensional mismatch, where electrons live in (2+1)D while photons propagate in (3+1)D. In order to define an action in (2+1)D, one may perform a dimensional reduction of quantum electrodynamics in (3+1)D (QED4) into Pseudo quantum electrodynamics (PQED). The main difference between this model and QED4 is the presence of a pseudo-differential operator in the Maxwell term. However, besides the Coulomb repulsion, electrons in a material are subjected to several microscopic interactions, which are inherent in a many-body system. These are expected to reduce the range of the Coulomb potential, leading to a short-range interaction. Here, we consider the coupling to a scalar field in PQED for explaining such mechanism, which resembles the spontanoues symmetry breaking (SSB) in Abelian gauge theories. In order to do so, we consider two cases: (i) By coupling the gauge field to a Higgs field in scalar quantum electrodynamics in (3+1)D and, thereafter, performing the dimensional reduction and; (ii) By coupling a Higgs field to the gauge field in PQED and subsequently calculating its effective potential. In case (i), we obtain a model describing electrons interacting through the Yukawa potential and, in case (ii), we show that SSB does not occur at one-loop approximation. The relevance of the model for describing electronic interactions in two-dimensional materials is also adressed.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
