Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2, Number 4 (2002), 163-197.
Relativistic wave equations with fractional derivatives and pseudodifferential operators
We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator . The equations corresponding to and (Klein-Gordon and Dirac equations) are local in their nature, but the multicomponent equations for arbitrary 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 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.
J. Appl. Math., Volume 2, Number 4 (2002), 163-197.
First available in Project Euclid: 30 March 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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