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 (□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 no...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X02110102 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545428194721792 |
|---|---|
| author | Petr Závada |
| author_facet | Petr Závada |
| author_sort | Petr Závada |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-424ed0e46e174e8e84139f869a7deba8 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-424ed0e46e174e8e84139f869a7deba82025-02-03T07:25:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422002-01-012416319710.1155/S1110757X02110102Relativistic wave equations with fractional derivatives and pseudodifferential operatorsPetr Závada0Institute of Physics, Academy of Sciences of Czech Republic, Na Slovance 2, Prague 8 CZ-182 21, Czech RepublicWe 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.http://dx.doi.org/10.1155/S1110757X02110102 |
| spellingShingle | Petr Závada Relativistic wave equations with fractional derivatives and pseudodifferential operators Journal of Applied Mathematics |
| title | Relativistic wave equations with fractional derivatives and
pseudodifferential operators |
| title_full | Relativistic wave equations with fractional derivatives and
pseudodifferential operators |
| title_fullStr | Relativistic wave equations with fractional derivatives and
pseudodifferential operators |
| title_full_unstemmed | Relativistic wave equations with fractional derivatives and
pseudodifferential operators |
| title_short | Relativistic wave equations with fractional derivatives and
pseudodifferential operators |
| title_sort | relativistic wave equations with fractional derivatives and pseudodifferential operators |
| url | http://dx.doi.org/10.1155/S1110757X02110102 |
| work_keys_str_mv | AT petrzavada relativisticwaveequationswithfractionalderivativesandpseudodifferentialoperators |