  In a classical theory of gravity, the Barbero-Immirzi parameter ($\eta$)
appears as a topological coupling constant through the Lagrangian density
containing the Hilbert-Palatini term and the Nieh-Yan invariant. In a quantum
framework, the topological interpretation of $\eta$ can be captured through a
rescaling of the wavefunctional representing the Hilbert-Palatini theory, as in
the case of the QCD vacuum angle. However, such a rescaling cannot be realized
for pure gravity within the standard (Dirac) quantization procedure where the
second-class constraints of Hilbert-Palatini theory are eliminated beforehand.
Here we present a different treatment of the Hilbert-Palatini second-class
constraints in order to set up a general rescaling procedure (a) for gravity
with or without matter and (b) for any choice of gauge (e.g. time gauge). The
analysis is developed using the Gupta-Bleuler and the coherent state
quantization methods.
