Relativistic wave equations with fractional derivatives andpseudodifferential operators
Petr Závada
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Source: Crossref
Published: Jan 1, 2002
DOI: 10.1155/s1110757x02110102
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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.
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