Solutions for the Lévy-Leblond or parabolic Dirac equation and its generalizations

@article{Bao2019SolutionsFT,
  title={Solutions for the L{\'e}vy-Leblond or parabolic Dirac equation and its generalizations},
  author={Sijia Bao and Denis Constales and Hendrik De Bie and Teppo Mertens},
  journal={Journal of Mathematical Physics},
  year={2019}
}
In this paper we determine solutions for the Levy-Leblond operator or a parabolic Dirac operator in terms of hypergeometric functions and spherical harmonics. We subsequently generalise our approach to a wider class of Dirac operators depending on 4 parameters. 

On fractional semidiscrete Dirac operators of L\'evy-Leblond type

In this paper we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators of L´evy-Leblond type on the semidiscrete space-time lattice h Z n × [0 , ∞ ) ( h > 0),

References

SHOWING 1-10 OF 34 REFERENCES

Fischer decomposition and special solutions for the parabolic Dirac operator

In this paper we study a Fischer decomposition for the parabolic Dirac operator which factorizes the heat equation. Since the standard construction techniques are not valid in our case, due to the

Explicit solutions of the inhomogeneous dirac equation

In this paper we establish a general principle which may be used to construct many explicit solutions to special inhomogeneous Dirac equations with distributional right-hand side. These solutions are

A function theory for the operator D-λ

In this paper the general solution of the equation (D − λ)w = 0 in SO(m)-invariant open subsets όmega of Rm is obtained, whereby D is the Dirac operator and λ is a complex constant. The results thus

Parabolic Dirac operators and the Navier–Stokes equations over time‐varying domains

We consider parabolic Dirac operators which do not involve fractional derivatives and use them to show the solvability of the in‐stationary Navier–Stokes equations over time‐varying domains.

Generalized supersymmetry and the Lévy-Leblond equation

Symmetries of the Levy-Leblond equation are investigated beyond the standard Lie framework. It is shown that the equation has two remarkable symmetries. One is given by the super Schrodinger algebra

Fundamental solutions for operators which are polynomials in the Dirac operator

In this paper we give explicit formulae — and this by a step by step procedure — for fundamental solutions of Spin(m)-invariant operators of the form \( \mathop \sum \nolimits_{k = 0}^n \) being the

Structure of solutions of polynomial Dirac equations in Clifford analysis

In this note, structures of null solutions of the polynomial Dirac operators D−λ Dk , are studied, where D is the Dirac operator in is the identity operator. Explicit decompositions of null solutions

Solutions for the Hyperbolic Dirac Equation on R1, m

In this article the hyperbolic unit ball in R m will be identified with the manifold of rays in the future null cone in R m+1. By means of the induced Clifford algebra structure there, one can

Explicit representations of the regular solutions to the time‐harmonic Maxwell equations combined with the radial symmetric Euler operator

In this paper we consider a generalization of the classical time‐harmonic Maxwell equations, which as an additional feature includes a radial symmetric perturbation in the form of the Euler operator

Cauchy-Green type formulae in Clifford analysis

A Cauchy integral formula is constructed for solutions to the polynomial Dirac equation (Dk + EkjbmDmn)f = 0, where each bm is a complex number, D is the Dirac operator in Rn , and f is defined on a