The gauge symmetries of firstorder general relativity with matter fields
Abstract
In ndimensional spacetimes (n > 3), there exists an internal gauge symmetry of the Palatini action with a cosmological constant that is the natural generalization of the socalled ‘local translations’ of threedimensional general relativity. We report the extension of this symmetry to include the minimal coupling of YangMills and fermion fields to the Palatini action with a cosmological constant. We show that, as in the case of threedimensional local translations, the extended symmetry depends on the energymomentum tensor of the corresponding matter field and, for fermions, it contains an additional term that in four dimensions is proportional to the axial fermion current. We also report the extension of the analog of this internal gauge symmetry for the Holst action with a cosmological constant by incorporating minimally coupled scalar and YangMills fields, as well as a nonminimally coupled fermion field. In the last case, the extended symmetry is affected by both the Immirzi parameter and the energymomentum tensor and, for fermions, it also depends on the axial fermion current.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 October 2018
 DOI:
 10.1088/13616382/aae10d
 arXiv:
 arXiv:1809.10729
 Bibcode:
 2018CQGra..35t5005M
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 It matches published version