A higher-derivative classical nonrelativistic U (1) × U (1) gauge field model that describes the topologically massive electromagnetic interaction of composite particles in 2+1 dimensions is proposed. This is made by adding a suitable higher-derivative term for the electromagnetic field to the Lagrangian of a model previously proposed. The model contains a Chern–Simons U(1) field and the topologically massive electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev–Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. The use of the higher-derivative term eliminates in the Landau gauge the ultraviolet divergence of the primitively divergent Feynman diagrams where the electromagnetic field propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the Becchi–Rouet-Stora–Tyutin algorithm is applied to the model.
The Canonical Quantization of the Free Electromagnetic Field in the Landau Gauge
