New solutions of the Dirac, Maxwell and Weyl equations from the
fractional Fourier transform
- URL: http://arxiv.org/abs/2101.03325v1
- Date: Sat, 9 Jan 2021 09:41:46 GMT
- Title: New solutions of the Dirac, Maxwell and Weyl equations from the
fractional Fourier transform
- Authors: Iwo Bialynicki-Birula
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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