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Third order wave equation in Duffin-Kemmer-Petiau theory: Massive case

Авторы: Markov Yu.A., Markova M.A., Bondarenko A.I.

Журнал: Physical Review D

Том: 92

Номер:

Год: 2015

Отчётный год: 2015

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Аннотация: Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [1] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q-commutator (q is a primitive cubic root of unity) and a new set of matrices eta(mu) instead of the original matrices beta(mu) of the DKP algebra are introduced. It is shown that in terms of these eta(mu) matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z -> q, where z is some complex deformation parameter entering into the definition of the.-matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function psi(x; z) is performed and it is shown that the solution is singular in the z -> q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.

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