Fermions, Mass-Gap and Landau Levels: Gauge invariant Hamiltonian for QCD in D=2+1

Abstract

A gauge-invariant reformulation of QCD in three spacetime dimensions is presented within a Hamiltonian formalism, extending previous work to include fermion fields in the adjoint and fundamental representations. A priori there are several ways to define the gauge-invariant versions of the fermions; a consistent prescription for choosing the fermionic variables is presented. The fermionic contribution to the volume element of the gauge orbit space and the gluonic mass-gap is computed exactly and this contribution is shown to be closely related to the mechanism for induction of Chern-Simons terms by parity-odd fermions. The consistency of the Hamiltonian scheme with known results on index theorems, Landau Levels and renormalization of Chern-Simons level numbers is shown in detail. We also comment on the fermionic contribution to the volume element in relation to issues of confinement and screening.