Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids
Abstract
The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphenelike materials, the surface states of some topological insulators, and possibly halffilled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the BogoliubovParasiukHeppZimmermann prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultrarelativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity C^{*}=(92 9 π^{2})/(18 π ) and the anomalous dimension of the fermion field γ_{ψ}(α ¯ ,ξ )=2 α ¯ (1 3 ξ )/3 16 (ζ_{2}N_{F}+4 /27 ) α^{¯ 2}+O (α^{¯ 3}) , where α ¯=e^{2}/(4 π )^{2} and ξ is the gaugefixing parameter.
 Publication:

Physical Review D
 Pub Date:
 April 2018
 DOI:
 10.1103/PhysRevD.97.074004
 arXiv:
 arXiv:1801.10385
 Bibcode:
 2018PhRvD..97g4004T
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 (v2) Published in PRD. Some references added. No change in results. (v1) LaTeX file with feynMF package. 15 pages, 4 figures