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21 August 2002 Relativistic wave equations with fractional derivatives and pseudodifferential operators
Petr Závada
J. Appl. Math. 2(4): 163-197 (21 August 2002). DOI: 10.1155/S1110757X02110102


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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Petr Závada. "Relativistic wave equations with fractional derivatives and pseudodifferential operators." J. Appl. Math. 2 (4) 163 - 197, 21 August 2002.


Published: 21 August 2002
First available in Project Euclid: 30 March 2003

zbMATH: 1007.81043
MathSciNet: MR1948084
Digital Object Identifier: 10.1155/S1110757X02110102

Primary: 15A66 , 81R20
Secondary: 26A33 , 34B27 , 47G30

Rights: Copyright © 2002 Hindawi

Vol.2 • No. 4 • 21 August 2002
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