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If the Einstein-Hilbert action ${\cal L}_{\rm EH}\propto R$ is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field $h^\alpha{}_\mu$, and the gauge field of local Lorentz transformations, the spin connection $A_{\mu \alpha}{}^ \beta $, there exists a new gauge symmetry which permits reshuffling the torsion, partially or totally, into the Cartan curvature term of the Einstein tensor, and back, via a {\em new multivalued gauge transformation\/}.
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We ignore here the second elastic constant since it is irrelevant to the argument
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The new freedom brought about by multivalued gauge transformations in many areas of physics is explained in the textbook MVF . For instance, we can derive
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2010
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