Relativistic wave equations with fractional derivatives and pseudodifferential operators

Petr Závada

Journal of Applied Mathematics, 2002, vol. 2, 1-35

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.

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:834729

DOI: 10.1155/S1110757X02110102

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