2008/01/31 by NIKODEM J. POPŁAWSKI, Nikodem J. Poplawski · 35 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Connection (principal bundle) #Covariant transformation #Electromagnetic field #Electromagnetic tensor #Electromagnetism #Quantum and Classical Electrodynamics #Scalar (mathematics) #Spin connection #Spinor #Spinor field #Tetrad #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0217732309030151
published in Modern Physics Letters A 24(06), 431-442 (World Scientific) · 8 pages; published version
openalex publication_date 2009/02/28 · arxiv created 2010/11/13 · arxiv updated 2011/06/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic fields is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational principle with the tetrad and spin connection as dynamical variables and show that, in this approach, the field equations are the Einstein–Maxwell equations if we relate the electromagnetic potential to the trace of the spin connection. We also show that, as in the Ponomarev–Obukhov formulation, the generally covariant Dirac Lagrangian gives rise to the standard spinor source for the Einstein–Maxwell equations, while the spinor field obeys the nonlinear Heisenberg–Ivanenko equation with the electromagnetic coupling. We generalize that formulation to spinors with arbitrary electric charges.