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arXiv · hep-th/9402033

The Lagrangian of q-Poincare' Gravity

Leonardo Castellani
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Abstract

The gauging of the q-Poincaré algebra of ref. hep-th 9312179 yields a non-commutative generalization of the Einstein-Cartan lagrangian. We prove its invariance under local q-Lorentz rotations and, up to a total derivative, under q-diffeomorphisms. The variations of the fields are given by their q-Lie derivative, in analogy with the q=1 case. The algebra of q-Lie derivatives is shown to close with field dependent structure functions. The equations of motion are found, generalizing the Einstein equations and the zero-torsion condition.

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Leonardo Castellani. 1994-02-17. The Lagrangian of q-Poincare' Gravity. https://doi.org/10.1016/0370-2693(94)91522-9

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