  In this paper, the connection between the path integral representation of
propagators in the coherent state basis with additional degrees of freedom
\cite{rohwer} and the one without any such degrees of freedom \cite{sgfgs} is
established. We further demonstrate that the path integral formalism developed
in the noncommutative plane using the coherent state basis leads to a quantum
mechanics involving a Chern-Simons term in momentum which is of noncommutative
origin. The origin of this term from the Bopp-shift point of view is also
investigated. A relativistic generalization of the action derived from the path
integral framework is then proposed. Finally, we construct a map from the
commutative quantum Hall system to a particle in a noncommutative plane moving
in a magnetic field. The value of the noncommutative parameter from this map is
then computed and is found to agree with previous results.
