New solutions of the Dirac, Maxwell and Weyl equations from the fractional Fourier transform
arXiv:2101.03325 · doi:10.1103/PhysRevD.103.085001
Abstract
New solutions of relativistic wave equations are obtained in a unified manner from generating functions of spinorial variables. The choice of generating functions as Gaussians leads to representations in the form of generalized fractional Fourier transforms. Wave functions satisfying the Dirac, Maxwell, and Weyl equations are constructed by simple differentiations with respect to spinorial arguments. In the simplest case, one obtains Maxwell and Dirac hopfion solutions.
arXiv comment3 figures
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