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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/S1110757X02110102 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |