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Relativistic wave equations with fractional derivatives and pseudodifferential operators

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  • Petr Závada

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.

Suggested Citation

  • Petr Závada, 2002. "Relativistic wave equations with fractional derivatives and pseudodifferential operators," Journal of Applied Mathematics, Hindawi, vol. 2, pages 1-35, January.
    • Handle: RePEc:hin:jnljam:834729
    DOI: 10.1155/S1110757X02110102
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