Quantum formalism for the electromagnetic interaction of composite particles in higher-derivative nonrelativistic gauge field models

Abstract

A comparative analysis between two correlated models of composite particles is performed. These
are higher-derivative nonrelativistic U(1)U(1) gauge eld models for the electromagnetic interac-
tion of these particles in (2+1) dimensions. The models contain a Chern-Simons U(1) eld and the
electromagnetic eld, and they describe both a composite boson system or a composite fermion one.
The second case is explicitly considered. The comparison is established on the results obtained ac-
cording to three formalisms of quantization: the canonical, following the usual Hamiltonian method
for singular higher-derivative systems, that of the Feynman path integral, extending the Faddeev-
Senjanovic algorithm, and the one obtained generalizing the Becchi-Rouet-Stora-Tyutin formalism.