Relativistic wave equations with fractional derivatives and pseudodifferential operators

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. Copyright © 2002 Hindawi Publishing Corporation. All rights reserved.