On the quantum properties of graphene-like quantum electrodynamics - Miranda, Émerson da Silva (2021)
First, in Part I we study a Lorentz invariant version of a mass-gap graphene-like planar quantum electrodynamics, the parity-preserving U(1) x U(1) massive QEDs. In Chapter 3, was showed it exhibits attractive interaction in low-energy electron-polaron-electron- polaron s-wave scattering, favoring quasiparticles bound states, the s-wave bipolarons. Still in Part I in Chapter 4, was verified that the model is ultraviolet finiteness — exhibits vanishing 5-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. It was done adopting the Becchi-Rouet-Stora (BRS) algebraic renormalization method in the framework of Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) subtraction scheme. In the sequence, in Part II of the thesis, we deal with the parity-preserving U(1) x U(1) hybrid QEDs, proposed as a pristine graphene-like planar quantum elec- trodynamics model. In Chapter 5 was determined the spectrum as well as 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, besides that, was verified it exhibits zero-energy Landau level indicating a kind of anomalous quantum Hall effect. Furthermore, the electron-polaron-electron-polaron scattering potentials in s- and p-wave states mediated by photon and Néel quasiparticles might exhibit attractive (s-wave state) or repulsive (p-wave state) interactions. Already in Chapter 6 was analyzed the quantum parity conservation at all orders in perturbation theory for the hybrid model. It was proved, by using the Lowenstein-Zimmermann (LZ) subtraction scheme, that the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, preserves parity for the model. To finalize the Part II, in Chapter 7, was showed the vanishing of the 8-functions associated to the coupling constants (0. = O and 8, = 0), the mass parameter (8,,) and the anomalous dimensions of all fields (y4, = 0), as well as the absence of parity and gauge anomalies at all orders of perturbation theory. Closing the analysis of the UA(1) x Us(1) hybrid QEDs it is ultraviolet and infrared finite at all orders in perturbation theory. Keywords: Quantum Hall effect. Graphene. Three space-time dimensions. Algebraic renormalization. Quantum Electrodynamics.