Quantum Field Formalism for the Electromagnetic Interaction of Composite Particles in a Nonrelativistic Gauge Model II

By generalizing a model previously proposed, a classical nonrelativistic U(1)×U(1) gauge field model for the electromagnetic interaction of composite particles in (2+1) dimensions is constructed. The model contains a Chern–Simons U(1) field and the electromagnetic U(1) field, and it describes both a composite boson system or a composite fermion one. The second case is considered explicitly. The model includes a topological mass term for the electromagnetic field and interaction terms between the gauge fields. By following the Dirac Hamiltonian formalism for constrained systems, the canonical quantization for the model is realized. By developing the path integral quantization method through the Faddeev–Senjanovic algorithm, the Feynman rules of the model are established and its diagrammatic structure is discussed. The Becchi–Rouet–Stora–Tyutin formalism is applied to the model. The obtained results are compared with the ones corresponding to the previous model.