The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations are solved exactly on the background of simplest static cosmological model, space of constant curvature of Riemann parameterized by spherical coordinates. Separation of variables is realized in the basis of Schrödinger- Pauli type, description of angular dependence in electromagnetic filed functions is given in terms of Wigner D-functions. A discrete frequency spectrum for electromagnetic modes depending on the curvature radius of space and three discrete parameters is found. 4-potentials for spherical electro- magnetic waves of magnetic and electric type have been constructed.
Comment on "Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential"
结果表明，Merad和Bensaid的论文“波函数for a Duffin-Kemmer-Petiau particle in a time-dependent potential”[J.Math.Phys.48，073515（2007）]在不需要厄米特哈密顿量的形式中无意中使用了非厄米特哈密顿量是不正确的。
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
We show that the Duffin-Kemmer-Petiau equation, minimally coupled to an Abelian gauge field, can be regarded as a matrix equation for the gauge potential produced internally from the matter fields. This can be solved as a rational expression in terms of currents bilinear in the matter wavefunction, together with a similar expression for the field strength tensor, thus providing a gauge invariant formulation of the self-interacting DKP equations. We give the derivation of this result for the 5 component DKP system, by analogy with the Dirac equation case. To this end, we establish the algebraic…
In the last years several papers addressed the supposed spin-1 sector of the massive Duffin-Kemmer-Petiau (DKP) equation restricted to (1+1) space-time dimensions. In this note we show explicitly that this is a misleading approach, since the DKP algebra in (1+1) dimensions admits only a spin-0 representation. Our result also is useful to understand why several recent papers found coincident results for both spin-0 and spin-1 sectors of the DKP theory in (3+1) dimensions when the dynamics is restricted to one space dimension.
We revisit the (2+1)-dimensional DKP oscillator in an external magnetic field by means of 4x4 and 6x6 representations of the DKP field, thus obtaining several cases studied in the literature. We found an splitting in the frequency of the DKP oscillator according to the spin projection that arises as an interplay between the oscillator, the external field and the spin, from which the energies and the eigenfunctions are expressed in a unified way. For certain critical values of the magnetic field the oscillation in the components of spin projections -1 and 1 is cancelled. We study the thermodyna…
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism with a deformation, an approach to the construction of the path integral representation in parasuperspace for the Green's function of a spin-1 massive particle in external Maxwell's field is developed. For this purpose a connection between the deformed DKP-algebra and an extended system of the parafermion trilinear commutation relations for the creation and annihilation operators $a^{\pm}_{k}$ and for an additional operator $a_{0}$ obeying para-Fermi statistics of order 2 based on the Lie algebra $\mathfrak{so}(2M+2)$ is establis…
This paper is an immediate continuation of the first part of our paper [1]. Here, in a para-Grassmann algebra we introduce a noncommutative, associative star product $*$ (the Moyal product), which is a direct generalization of the star product in the algebra of Grassmann numbers. Isomorphism between the algebra of para-Grassmann numbers of order 2 equipped with the star product and with the algebra of creation and annihilation operators $a_{n}^{\pm}$ obeying the para-Fermi statistics of the same order is established. Two independent approaches to the calculation of the Moyal product $*$ are co…
In this paper, we investigate the Duffin-Kemmer-Petiau (DKP) equation for spin-zero system of charge-free particles in the background of a flat class of Gödel-type space-times, and evaluate the individual energy levels and corresponding wave-functions, in details.
We study analytically the two dimensional deformed bosonic oscillator equations for charged particles (both spin 0 and spin 1 particles) subject to the effect of a uniform magnetic field. We consider the presence of a minimal uncertainty in momentum caused by the Anti-deSitter model and we use the Nikiforov-Uvarov method to solve the system. The exact energy eigenvalues and the corresponding wave functions are analytically obtained for both Klein-Gordon and scalar Duffin-Kemmer-Petiau cases. For spin 1 DKP case, we deduce the behaviour of the DKP equation and write the non-relativistic energie…
From the Killing spinor equation and the equations satisfied by their bilinears we deduce some well known bosonic and fermionic field equations of mathematical physics. Aside from the trivially satisfied Dirac equation, these relativistic wave equations in curved spacetimes respectively are Klein-Gordon, Maxwell, Proca, Duffin-Kemmer-Petiau, Kähler, twistor and Rarita-Schwinger equations. This result shows that, besides being special kinds of Dirac fermions, Killing fermions can be regarded as physically fundamental. For the Maxwell case the problem of motion is analysed in a reverse manner wi…
