The method of uniqueness and the optical conductivity of graphene: new application of a powerful technique for multi-loop calculations

Abstract

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation of a two-loop massless propagator Feynman diagram with a non-integer index on the central line. The result is applied to the computation of the optical conductivity of graphene at the infra-red Lorentz invariant fixed point. The effect of counter-terms is analysed. A brief comparison with the non-relativistic case is included.

Prepared for the Vth International Conference "Models in Quantum Field Theory" dedicated to Prof. Aleksandr Nikolaevich Vasiliev. LaTeX file with feynMF package. 15 pages, 4 figures (v2) Minor modifications (some per referee's comments)

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• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Field theoretic renormalization study of interaction corrections to the universal ac conductivity of graphene
• Landau-Khalatnikov-Fradkin transformation of the fermion propagator in massless reduced QED
• Chiral symmetry restoration in RQED at finite temperature in the supercritical coupling regime
• Effects of the Pseudo-Chern-Simons action for strongly correlated electrons in the plane
• Defect QED: Dielectric without a Dielectric, Monopole without a Monopole