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Journal of Applied Mathematics
Volume 2 (2002), Issue 4, Pages 163-197
http://dx.doi.org/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 Hindawi Publishing Corporation. 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.