Analysis of quantum electrodynamics models with applications to two-dimensional condensed matter phenomena - Lima, Lázaro Souza (2023)
In this work, two planar quantum electrodynamics (QED3 ) models with applications to condensed matter phenomena are analyzed. The ﬁrst one, discussed in Chapter 2, has possible applications to the fractional quantum Hall eﬀect. A fundamental analysis is per- formed in order to verify the physical consistency of the model. It is found that unitarity is jeopardized, and it is checked that the bosons of the model are non-fundamental. A diagonalization procedure of the action is performed, aiming to identify the fundamental ones and it is veriﬁed that the action written in terms of them is physically consistent. The other model analyzed is a parity-preserving QED3 , which yields theoretical results that mimic some experimental observations performed in pristine graphene. In chapter 3, it is veriﬁed that the BPHZL renormalization procedure preserves parity in this model. In chapter 4, this model is renormalized at 2-loops order, by BPHZL. In chapter 5, the alge- braic renormalization scheme allows to verify that the parity preserving QED3 is free from anomalies and it presents a quantum scale invariance, which is another feature observed in pristine graphene. Keywords: Quantum Electrodynamics; Three Space-Time Dimensions; Algebraic Renor- malization; Condensed Matter.