Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third order wave equation in Duffin-Kemmer-Petiau theory. Massive case   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.

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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
2
The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn