Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case
| Autor: | Markov, Yu. A., Markova, M. A., Bondarenko, A. I. |
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| Rok vydání: | 2015 |
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| Zdroj: | Phys. Rev. D 92, 105017 (2015) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.92.105017 |
| Popis: | 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 [Phys.Lett.A {\bf 244} (1998) 329] 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 $z \rightarrow q$, where $z$ is some complex deformation parameter entering into the definition of the $\eta$ - 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 $z \rightarrow q$ 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. Comment: 39 pages |
| Databáze: | arXiv |
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