We investigate the effects of (Curvature) 2 -and (Torsion) 2 -terms in the Einstein-Hilbert-Chern-Simons Lagrangian. The purposes are two-fold: (i) to show the efficacy of an orthogonal basis of degree-of-freedom projection operators recently proposed and to ascertain its adequacy for obtaining propagators of general parity-breaking gravity models in three dimensions; (ii) to analyze the role of the topological Chern-Simons term for the unitarity and the particle spectrum of the model squared-curvature terms in connection with dynamical torsion. Our conclusion is that the Chern-Simons term does not influence the unitarity conditions imposed on the parameters of the Lagrangian, but significantly modifies the particle spectrum. * Electronic address: helayel@cbpf.br † Electronic address: carlos@cbpf.br ‡ Electronic address: bpdias@cbpf.br § Electronic address: alfredov@cbpf.br ¶ Electronic address: vjose@cbpf.br

Canonical quantization is reviewed here for the Abelian Lee-Wick model by using the Dirac constraints method, a Gupta-Bleuler-like prescription is implemented and the BRST charge operator for this model is built. New degrees of freedom associated to the (higher derivatives) Lee-Wick ghost are excluded from the (physical) space of observables by the imposition of a Piguet-Nielsen-type BRST-extended symmetry for the Lee-Wick mass term, removing the Lee-Wick mass parameter of the theory, which implies remove all the higher-derivative sector. In addition, another prescription based on a new subsidiary condition of invariance under a purely higher-derivative BRST-type new symmetry is proposed.