Introducing matter fields in model of noncommutative gravity

Theory founded on SO(2,3)* gauge symmetry. One significant feature of thisapproach is that gravitational field, given by the vierbein, becomesmanifest only after a suitable gauge fixing and it is formally united withother gauge fields. Starting from a model of pure noncommutative gravity, weextend it by introducing fermions and Yang-Mills gauge field. Using theenveloping algebra approach and the Seiberg-Witten map we constructcorresponding actions and expand them perturbatively in powers of thecanonical noncommutativity parameter θαβ. Unlike in the case of purenoncommutative gravity, first non-vanishing noncommutative corrections arelinear in the noncommutativity parameter and they describe the coupling ofmatter and gauge fields with gravity due to spacetime noncommutativity. Thisis augmented by the fact that some of these corrections pertain even in flatspacetime where they induce potentially observable noncommutativedeformations. We discuss the effects of noncommutativity on electron’sdispersion relation in the presence of constant background magnetic field -Landau levels. Our results could be useful for further investigation ofphenothe menological consequences of spacetime noncommutativity. [Project ofthe Serbian Ministry of Education, Science and Technological Development,Grant no. ON171031]