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.
Publié le : 2002-05-14
Classification:
81R20,
15A66,
47G30,
26A33,
34B27
@article{1049074993,
author = {Z\'avada, Petr},
title = {Relativistic wave equations with fractional derivatives and
pseudodifferential operators},
journal = {J. Appl. Math.},
volume = {2},
number = {8},
year = {2002},
pages = { 163-197},
language = {en},
url = {http://dml.mathdoc.fr/item/1049074993}
}
Závada, Petr. Relativistic wave equations with fractional derivatives and
pseudodifferential operators. J. Appl. Math., Tome 2 (2002) no. 8, pp. 163-197. http://gdmltest.u-ga.fr/item/1049074993/