Authors: Yu A Markov M A Markova A I Bondarenko
Publish Date: 2017/03/11
Volume: 59, Issue: 11, Pages: 1948-1955
Abstract
Within the framework of the Duffin–Kemmer–Petiau DKP formalism a consistent approach to derivation of the thirdorder wave equation is suggested For this purpose an additional algebraic object the socalled qcommutator q is a primitive cubic root of unity and a new set of matrices ημ instead of the original matrices βμ of the DKP algebra are introduced It is shown that in terms of these ηmatrices we have succeeded to reduce the procedure of the construction of cubic root of the thirdorder wave operator to a few simple algebraic transformations and to a certain operation of passage to the limit z → q where z is some complex deformation parameter entering into the definition of the ημmatrices A corresponding generalization of the result obtained to the case of interaction with an external electromagnetic field introduced through the minimal coupling scheme is performed 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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