https://doi.org/10.1140/epjc/s10052-023-11255-x
Regular Article - Theoretical Physics
Scale invariant Einstein–Cartan theory in three dimensions
1
Department of Physics, Istanbul Technical University, 34469, Istanbul, Maslak, Turkey
2
Department of Physics, Faculty of Science, Pamukkale University, Denizli, Turkey
Received:
14
December
2022
Accepted:
21
January
2023
Published online:
1
February
2023
We retreat the well-known Einstein–Cartan theory by slightly modifying the covariant derivative of spinor field by investigating double cover of the Lorentz group. We first write the Lagrangian consisting of the Einstein–Hilbert term, Dirac term and a scalar field term in a non-Riemannian spacetime with curvature and torsion. Then by solving the affine connection analytically we reformulate the theory in the Riemannian spacetime in a self-consistent way. Finally we discuss our results and give future perspectives on the subject.
© The Author(s) 2023
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