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E. S. Miranda

Publications and source records attributed to E. S. Miranda.

7 recordsLinked to original sources
arXiv2025

The BPHZL renormalization of a planar quantum electrodynamics up to 2-loops and beyond

The renormalization of a parity-even massless $U(1)\times U(1)$ quantum electrodynamics in three space-time dimensions (QED$_3$) is studied by adopting the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme to renormalize the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, moreover due to the model superrenormalizability the ultraviolet divergences are bounded up to 2-loops. Finally, through the BPHZL renormalization method together with the LZ subtraction scheme the ultraviolet and infrared finiteness of the model is proved up to 2-loops and beyond.

hep-th↗
arXiv2024

The spectrum consistency of fractional quantum Hall effect model

The spectrum consistency of the three fermion family $U(1)\times U(1)$ quantum electrodynamics in three space-time dimensions [Phys. Rev. Lett. 124 (2020) 131601] is analyzed. It has been verified that the originally proposed action violates the unitarity consistency condition in the gauge field sector by exhibiting negative norm states in the spectrum. However, the cure came through the fundamental gauge fields properly settled, consequently, the action rewritten in terms of those fundamental fields shows to be free from any spurious degrees of freedom, and the model now becomes safe for further quantization.

hep-th↗
arXiv2021

On the ultraviolet finiteness of parity-preserving $U(1) \times U(1)$ massive QED$_3$

The parity-preserving $U_A(1)\times U_a(1)$ massive QED$_3$ is ultraviolet finiteness -- exhibits vanishing $β$-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern-Simons mass parameter, and all the anomalous dimensions of the fields -- as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme.

hep-th↗
arXiv2020

Quantum parity conservation in planar quantum electrodynamics

Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even $U(1)\times U(1)$ planar quantum electrodynamics (QED$_3$) model. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme, in the framework of the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2-loops. Finally, it is proved that the BPHZL renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity-even $U(1)$ QED$_3$.

hep-th↗
arXiv2020

On the electron-polaron--electron-polaron scattering and Landau levels in pristine graphene-like quantum electrodynamics

The parity-preserving $U(1)\times U(1)$ massless QED$_3$ is proposed as a pristine graphene-like planar quantum electrodynamics model. The spectrum content, the degrees of freedom, spin, masses and charges of the quasiparticles (electron-polaron, hole-polaron, photon and Néel quasiparticles) which emerge from the model are discussed. The four-fold broken degeneracy of the Landau levels, similar as the one experimentally observed in pristine graphene submitted to high applied external magnetic fields, is obtained. Furthermore, the model exhibits zero-energy Landau level indicating a kind of anomalous quantum Hall effect. The electron-polaron--electron-polaron scattering potentials in $s$- and $p$-wave states mediated by photon and Néel quasiparticles are computed and analyzed. Finally, the model foresees that two electron-polarons ($s$-wave state) belonging to inequivalent $\mathbf{K}$ and $\mathbf{K^\prime}$ points in the Brillouin zone might exhibit attractive interaction, while two electron-polarons ($p$-wave state) lying both either in $\mathbf{K}$ or in $\mathbf{K^\prime}$ points experience repulsive interaction.

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