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In condensed matter, crystal with disclination and dislocation has both curvature and torsion. I am looking for a reference in which path integral quantization of Dirac equation on manifold with curvature and torsion was discussed.

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I wasn't aware of the name "Einstein-Cartan manifold" but if it is common usage, surely it wouldn't simply mean a manifold with nonzero torsion, surely it would be a manifold arising from the EC theory itself? –  WetSavannaAnimal aka Rod Vance Sep 17 '13 at 8:15

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