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Abstract
We use the Euler-Lagrange equations of motion in order to solve the constraints for various types of two dimensional U(1) gauge theories. It is shown that, using this method, one obtains a Lagrangian which is gauge independent. In particular, we discuss the anyonic behavior of theories which contain fermions coupled to the Chern-Simons term, with and without the Maxwell kinetic energy term. The existence of braid statistics for the free fermions in the adiabatic limit is discussed, as part of a consistent perturbative expansion around this limit.
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