Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields

@article{Fatibene2014SymmetryOA,
  title={Symmetry operators and separation of variables for Dirac's equation on two-dimensional spin manifolds with external fields},
  author={Lorenzo Fatibene and Raymond G. McLenaghan and Giovanni Rastelli},
  journal={arXiv: Mathematical Physics},
  year={2014}
}
The second order symmetry operators that commute with the Dirac operator with external vector, scalar and pseudo-scalar potentials are computed on a general two-dimensional spin-manifold. It is shown that the operator is defined in terms of Killing vectors, valence two Killing tensors and scalar fields defined on the background manifold. The commuting operator that arises from a non-trivial Killing tensor is determined with respect to the associated system of Liouville coordinates and compared… 

References

SHOWING 1-10 OF 29 REFERENCES

Matrix operator symmetries of the Dirac equation and separation of variables

The set of all matrix‐valued first‐order differential operators that commute with the Dirac equation in n‐dimensional complex Euclidean space is computed. In four dimensions it is shown that all

Symmetry operators for Dirac's equation on two-dimensional spin manifolds

It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence 2 Killing tensors. The

Separation of Variables for Systems of First-Order Partial Differential Equations and the Dirac Equation in Two-Dimensional Manifolds

The problem of solving the Dirac equation on two-dimensional manifolds is approached from the point of separation of variables, with the aim of creating a foundation for analysis in higher

Non-factorizable separable systems and higher-order symmetries of the Dirac operator

  • M. FelsN. Kamran
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1990
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

Killing Tensor Quantum Numbers and Conserved Currents in Curved Space

The relationship between relativistic quantum current conservation laws in a curved-space background and the corresponding "good quantum numbers," i.e., operators that commute with the fundamental

Complex variables for separation of the Hamilton-Jacobi equation on real pseudo-Riemannian manifolds

In this paper the geometric theory of separation of variables for the time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on

Dirac equation in external vector fields: Separation of variables

The method of separation of variables in the Dirac equation in the external vector fields is developed through the search for exact solutions. The essence of the method consists of the separation of

Variable-separation theory for the null Hamilton–Jacobi equation

The theory of the separation of variables for the null Hamilton–Jacobi equation H=0 is systematically revisited and based on Levi–Civita separability conditions with Lagrangian multipliers. The

The Dirac equation in external fields: Variable separation in Cartesian coordinates

The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 3 0, 2132 (1989)] is developed for the complete set of