Journal of Applied Mathematics
Volume 2 (2002), Issue 4, Pages 163-197
doi:10.1155/S1110757X02110102
Relativistic wave equations with fractional derivatives and
pseudodifferential operators
Institute of Physics, Academy of Sciences of Czech Republic, Na Slovance 2, Prague 8 CZ-182 21, Czech Republic
Received 17 October 2001
Copyright © 2002 Petr Závada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study the class of the free relativistic covariant equations
generated by the fractional powers of the d′Alembertian operator
(□1/n). The equations corresponding to n=1 and 2
(Klein-Gordon and Dirac equations) are local in their nature, but
the multicomponent equations for arbitrary n>2
are nonlocal. We
show the representation of the generalized algebra of Pauli and
Dirac matrices and how these matrices are related to the algebra
of SU (n)
group. The corresponding representations of the
Poincaré group and further symmetry transformations on the
obtained equations are discussed. The construction of the related
Green functions is suggested.