Journal of Applied Mathematics

Relativistic wave equations with fractional derivatives and pseudodifferential operators

Petr Závada

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2, Number 4 (2002), 163-197.

Dates
First available in Project Euclid: 30 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.jam/1049074993

Digital Object Identifier
doi:10.1155/S1110757X02110102

Mathematical Reviews number (MathSciNet)
MR1948084

Zentralblatt MATH identifier
1007.81043

Subjects
Primary: 81R20: Covariant wave equations 15A66: Clifford algebras, spinors
Secondary: 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx] 26A33: Fractional derivatives and integrals 34B27: Green functions

Citation

Závada, Petr. Relativistic wave equations with fractional derivatives and pseudodifferential operators. J. Appl. Math. 2 (2002), no. 4, 163--197. doi:10.1155/S1110757X02110102. https://projecteuclid.org/euclid.jam/1049074993


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