Pauli-type coupling between spinors and curved spacetime

Abstract

We investigate Pauli-type interactions generated by minimal coupling of a specified covariantly regular representative of the Dirac Lagrangian. A derivative-quadratic term proportional to a length parameter $\ell$ is a total divergence in free flat spacetime and leaves the free Dirac equation unchanged. After electromagnetic coupling, it is equivalent, up to a divergence, to a Pauli operator with coefficient $-q\ell /6$. We explain how a specified comparison between measured and predicted anomalous magnetic moments constrains this coefficient, separating historical illustrative scales from a conditional statistical bound. In metric-compatible Riemann--Cartan spacetime, the same construction generates torsion-dependent derivative couplings and a spin-curvature coupling. In the torsion-free limit, the latter reduces to the scalar mass coefficient $m+\ell R/12$. On prescribed pure-axial and pure-vector torsion backgrounds, the characteristic form admits superluminal wavefronts relative to the spacetime metric in its nonzero-torsion Lorentzian regime; sufficiently large spacelike effective torsion instead leads to degeneracy and an ultrahyperbolic characteristic form. For the observed cosmological constant and illustrative microscopic values of $\ell$, the vacuum mass correction is negligible. High-curvature applications and the characteristic structure of the full coupled theory require a specified gravitational action and further dynamical analysis.

23 pages

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Cited by in corpus (1)

• Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space