## Journal of Applied Mathematics

### Relativistic wave equations with fractional derivatives and pseudodifferential operators

#### Abstract

We study the class of the free relativistic covariant equations generated by the fractional powers of the d′Alembertian operator $(\square^{1/n})$. 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 $\mathrm{SU}(n)$ 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

https://projecteuclid.org/euclid.jam/1049074993

Digital Object Identifier
doi:10.1155/S1110757X02110102

Mathematical Reviews number (MathSciNet)
MR1948084

Zentralblatt MATH identifier
1007.81043

#### 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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