Jian Yang, Kinjal Banerjee, Yongge Ma
We study the coupling of the gravitational action, which is a linear combination of the Hilbert-Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing, which leads to a consistent geometrical dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a connection dynamical formalism of the theory can be obtained by a canonical transformation. Hence, the techniques of loop quantum gravity can be employed to quantize this Poincare gauge theory with non-zero torsion.
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http://arxiv.org/abs/1211.2377
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