Gauge theories in (2+1) dimensions and quantum Hall effect in higher dimensions

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Over the last few years the PI and collaborators, have developed a gauge invariant Hamiltonian analysis of Yang-Mill theory in two spatial dimensions. Several interesting results were derived such as an exact expression for the integration measure on the gauge invariant configuration space, an expression for the vacuum wave and an analytic formula for the string tension. Motivated by recent renewed interest in this topic, the PI proposes to analyze higher order corrections to the calculated string tension, investigate screening of adjoint matter versus confinement in this frame work and apply this Hamiltonian formulation to study issues of dynamical mass generation in (2+1) dimensional QED with massless fermions.