Geodesic
Kinetic term for the Lorentz connection
Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 108-118

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The most general five-parameter Lagrangian quadratic in the curvature giving the kinetic term for the Lorentz connection is considered. The canonical Hamiltonian is constructed in the tetrad and Lorentz connection variables and in the time gauge for the tetrad field. The condition that the quadratic lorm of the generalized momenta for the Lorentz connection be positive definite is used to find a two-parameter Lagrangian that is a sum of squares of the scalar curvature and the pseudoscalar dual to the curvature tensor. The primary constraints have the consequence that among the dynamical components of the Lorentz connection there remain only two scalar components of opposite parity. 
@article{TMF_1985_65_1_a10,
     author = {M. O. Katanaev},
     title = {Kinetic term for the {Lorentz} connection},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {108--118},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a10/}
}
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M. O. Katanaev. Kinetic term for the Lorentz connection. Teoretičeskaâ i matematičeskaâ fizika, Tome 65 (1985) no. 1, pp. 108-118. http://geodesic.mathdoc.fr/item/TMF_1985_65_1_a10/