Pauli-type coupling between spinors and curved spacetime

Understand

In this study we prove that the Pauli interaction -- which is associated with a length parameter -- emerges when the minimal coupling recipe is applied to the non-degenerate version of the Dirac Lagrangian.

• The conventional Dirac Lagrangian is rendered non-degenerate if supplemented by a particular term quadratic in the derivatives of the spinors.
• For dimensional reasons, this non-degenerate Dirac Lagrangian is associated with a length parameter $\ell$.
• It yields the standard free Dirac equation in Minkowski space.