Abstract
The Hamiltonian describing a composite fermion system is usually presented in a phenomenological way. By using a classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of electrons, we show how to obtain the mean-field Hamiltonian describing composite fermions in 2 + 1 dimensions. In order to achieve this goal, the Dirac Hamiltonian formalism for constrained systems is used. Furthermore, we compare these results with the ones corresponding to the inclusion of a topological mass term for the electromagnetic field in the Lagrangian.
Highlights
The study of low-dimensional electron systems is a topic of great current interest in condensed matter
By means of a classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of electrons, we have shown how to find the mean-field Hamiltonian describing composite fermions in 2 + 1 dimensions
In the usual formulation, Equation (22) is taken as a constraint of the theory
Summary
The study of low-dimensional electron systems is a topic of great current interest in condensed matter. [8] [9], we have proposed models of composite particles and we have studied them by using the first mechanism cited in the previous paragraph These models are generalizations of the models discussed by means of the second mechanism in Refs. By using the standard methods of field theory, we show that the same Hamiltonian can be reached. In this context, our purpose is to relate the results of Refs. We use the Dirac Hamiltonian formalism for constrained systems In this way, we show that this procedure leads to the same results as the ones obtained by means of the phenomenological models of condensed matter.
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