First-order symmetries of Dirac equation in curved background: a unified dynamical symmetry condition

Understand

It has been shown that, for all dimensions and signatures, the most general first-order linear symmetry operators for the Dirac equation including interaction with Maxwell field in curved background are given in terms of Killing-Yano (KY) forms.

• As a general gauge invariant condition it is found that among all KY-forms of the underlying (pseudo) Riemannian manifold, only those which Clifford commute with the Maxwell field take part in the symmetry operator.
• It is also proved that associated with each KY-form taking part in the symmetry operator, one can define a quadratic function of velocities which is a geodesic invariant as well as a constant of motion for the classical trajectory.
• Some geometrical and physical implications of the existence of KY-forms are also elucidated.