  The classical counterpart of noncommutative quantum mechanics is a
constrained system containing only second class constraints. The embedding
procedure formulated by Batalin, Fradkin and Tyutin (BFT) enables one to
transform this system into an Abelian gauge theory exhibiting only first class
constraints. The appropriateness of the BFT embedding, as implemented in this
work, is verified by showing that there exists a one to one mapping linking the
second class model with the gauge invariant sector of the gauge theory. As is
known, the functional quantization of a gauge theory calls for the elimination
of its gauge freedom. Then, we have at our disposal an infinite set of
alternative descriptions for noncommutative quantum mechanics, one for each
gauge. We study the relevant features of this infinite set of correspondences.
The functional quantization of the gauge theory is explicitly performed for two
gauges and the results compared with that corresponding to the second class
system. Within the operator framework the gauge theory is quantized by using
Dirac's method.
