Remarks on the Chern-Simons photon term in the QED description of graphene
David Dudal (Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium, KU Leuven Campus Kortrijk—Kulak, Department of Physics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium); Ana Júlia Mizher (KU Leuven Campus Kortrijk—Kulak, Department of Physics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium, Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271—Bloco II, 01140-070 Sáo Paulo, SP, Brazil); Pablo Pais (Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague 8, Czech Republic, KU Leuven Campus Kortrijk—Kulak, Department of Physics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium)
We revisit the Coleman-Hill theorem in the context of reduced planar QED. Using the global U(1) Ward identity for this nonlocal but still gauge-invariant theory, we can confirm that the topological piece of the photon self-energy at zero momentum does not receive further quantum corrections apart from the potential one-loop contribution, even when considering the Lorentz-noninvariant case due to the Fermi velocity . This is of relevance to probe possible time parity odd dynamics in a planar sheet of graphene which has an effective description in terms of ()-dimensional planar reduced QED.