Non-factorizable separable systems and higher-order symmetries of the Dirac operator. (English) Zbl 0727.35115
Summary: It is shown that there exist separable systems for the Dirac operator on four-dimensional lorentzian spin manifolds that are not factorizable in the sense of Miller. The symmetry operators associated to these new separable systems are of higher order than the Dirac operator. They are characterized in the second-order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions.
MSC:
35Q40 | PDEs in connection with quantum mechanics |
35Q75 | PDEs in connection with relativity and gravitational theory |
81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |