Fermionic matter coupled to higher derivative Chern–Simons theories. II

Abstract

The diagrammatic and the Feynman rules for the higher derivative Chern–Simons theories in (2+1) dimensions coupled to fermionic matter are constructed. This is done by starting from the path-integral quantization. Once the diagrammatic and the Feynman rules are given, the regularization and renormalization problem of this higher derivative model is analysed in the framework of the perturbation theory. The unitarity problem related with the possible appearance of ghost states with negative norm is also discussed. Finally, the BRST formalism for the model is constructed and some interesting differences with respect to the formalism applied to usual Chern–Simons models are presented.