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The Einstein-Cartan theory of gravitation is generalized by the addition of the most general action which is bilinear in the antisymmetric part of the connection and linear in the Levi-Civita density and hence contains both scalar and pseudoscalar contributions. For arbitrary-spin fields new tensor and pseudotensor interactions arise while for spin-1/2 fields the theory reduces to Cartan's equations, apart from a reduction in the spin-spin coupling constant.
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A. J. Purcell (1978) studied this question.
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