Relativistic wave equations with fractional derivatives and pseudo-differential operators

Details Relativistic wave equations with fractional derivatives and pseudo-differential operators Relativistic wave equations with fractional derivatives and pseudo-differential operators

2000-03-15

arxiv.org/abs/hep-th/0003126v2

J.Appl.Math.2:163-197,2002

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, Tex. In the corrected version a small bug in cross-references to some equations is removed. Minor text corrections a

Scientific paper

10.1155/S1110757X02110102

The class of the free relativistic covariant equations generated by the fractional powers of the D'Alambertian operator $(\square^{1/n})$ is studied. Meanwhile the equations corresponding to n=1 and 2 (Klein-Gordon and Dirac equations) are local in their nature, the multicomponent equations for arbitrary n>2 are non-local. It is shown, how the representation of generalized algebra of Pauli and Dirac matrices looks like and how these matrices are related to the algebra of SU(n) group. The corresponding representations of the Poincar\'e group and further symmetry transformations on the obtained equations are discussed. The construction of the related Green functions is suggested.

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