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A fractional Dirac equation and its solution

dc.contributor.authorMuslih, Sami I.
dc.contributor.authorAgrawal, Om. P.
dc.contributor.authorBaleanu, Dumitru
dc.date.accessioned2016-06-07T07:03:25Z
dc.date.available2016-06-07T07:03:25Z
dc.date.issued2010
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümüen_US
dc.description.abstractThis paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order a. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit a. 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanicsen_US
dc.description.publishedMonth2
dc.identifier.citationMuslih, S.I., Agrawal, Om P., Baleanu, D. (2010). A fractional Dirac equation and its solution. Journal of Physics A-Mathematical and Theoretical, 43(5). http://dx.doi.org/10.1088/1751-8113/43/5/055203en_US
dc.identifier.doi10.1088/1751-8113/43/5/055203
dc.identifier.issn1751-8113
dc.identifier.issue5en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/1036
dc.identifier.volume43en_US
dc.language.isoenen_US
dc.publisherIOP Publishing LTDen_US
dc.relation.ispartofJournal of Physics A-Mathematical and Theoreticalen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectEuler-Lagrange Equationsen_US
dc.subjectSequential Mechanicsen_US
dc.subjectLinear Velocitiesen_US
dc.subjectDerivativesen_US
dc.subjectFormulationen_US
dc.subjectFormalismen_US
dc.subjectSystemsen_US
dc.titleA fractional Dirac equation and its solutiontr_TR
dc.titleA Fractional Dirac Equation and Its Solutionen_US
dc.typeArticleen_US
dspace.entity.typePublication

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