Alternative Derivation of the Mean-Field Equations for Composite Fermions

Edmundo C. Manavella^1,2*, Carlos E. Repetto^1,2

¹Instituto de Física Rosario (CONICET-UNR), Rosario, Argentina.
²Facultad de Ciencias Exactas, Ingeniería y Agrimensura (UNR), Rosario, Argentina.

DOI: 10.4236/jmp.2015.612175                

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.

Keywords

Quantum Field Theory, Field Theories in Dimensions Other than Four, Chern-Simons Gauge Theory, Lagrangian and Hamiltonian Formalisms

Conflicts of Interest

The authors declare no conflicts of interest.

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