Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

Abstract

A higher-derivative classical nonrelativistic U(1) × U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2 + 1 dimensions is proposed. The model contains a Chern-Simons U(1) field and the electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. The model is obtained by adding suitable higher-derivative terms to the Lagrangian of a model previously proposed. One of them for the electromagnetic field and the other for the Chern-Simons field. 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. In this context, only a mixed bosonic propagator can be defined. The use of the higherderivative terms eliminates the ultraviolet divergence of the primitively divergent Feynman diagrams where the bosonic propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the BecchiRouet-Stora-Tyutin algorithm is applied to the model. We will focus our attention on the issue from the point of view of the field theory.