1997/07/24 by G. Bimonte, Bimonte, G., R. Musto +5
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #gr-qc #hep-th #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.hep-th/9707201
Latex file, 14 pages, no figures. Major changes in text. Contribution to the proceedings of the conference "Quantum Groups, Deformations and Contractions" Istanbul 1997, to be published in Turkish Journal of Physics. Title changed in journal to "The Quantum Poincare' Group as Hidden Symmetry of General Relativity"
Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group ISOq(3,1). Although the gauge fields, that is the spin--connection and the vierbeins are non--commuting objects depending on a deformation parameter, q, it is possible to construct out of them a metric theory which is insensitive to the deformation. The Christoffel symbols and the Riemann tensor are ordinary commuting objects. Hence it is argued that torsionless Einstein's General Relativity is the common invariant sector of a one--parameter family of deformed gauge theories.