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 thermodynamics of the canonical ensemble of the vectorial sector, where a phase transition is reported when the cancellation of the oscillation occurs. Thermodynamic potentials converge rapidly to their asymptotical expressions in the high temperature limit with the partition function symmetric under the reversion of the magnetic field.
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
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.
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。
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 this paper, we study the covariant Duffin-Kemmer-Petiau (DKP) equation in the space-time generated by a cosmic string and we examine the linear interaction of a DKP field with gravitational fields produced by topological defects and thus study the influence of topology on this system. We highlight two classes of solutions defined by the product of the deficit angle with the angular velocity of the rotating frame. We solve the covariant form of DKP equation in an exact analytical manner for node-less and one-node states by means of an appropriate ansatz.
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…
We solve the Duffin-Kemmer-Pétiau equation in the presence of a spatially one-dimensional symmetric potential well. We compute the scattering state solutions and we derive conditions for transmission resonances. The bound solutions are derived by a graphic study and the appearance of the antiparticle bound state is discussed.
The Aharonov-Bohm (AB) problem for vector bosons by the Duffin-Kemmer-Petiau (DKP) formalism is analyzed. Depending on the values of the spin projection, the relevant eigenvalue equation coming from the DKP formalism reveals an equivalence to the spin-$1/2$ AB problem. By using the self-adjoint extension approach, we examine the bound state scenario. The energy spectra are explicitly computed as well as their dependencies on the magnetic flux parameter and also the conditions for the occurrence of bound states.
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 present the exact solution of the three-dimensional Duffin--Kemmer--Petiau oscillator for both spin 0 and spin 1 cases, with the presence of minimal uncertainty in momentum in anti--de Sitter model. We use the representation of vector spherical harmonics and the Nikiforov--Uvarov method to determine exactly the energy eigenvalues and the eigenfunctions in all cases. Our study of the energy spectrum allows us to define a new interpretation of natural and unnatural parity states of the vector particle and we show the crucial role played by the spin--orbit coupling in this differentiation betw…
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…
The spin 1 particle is treated in the presence of the Dirac magnetic monopole in the Minkowski and Lobachevsky spaces. Separating the variables in the frame of the matrix 10-component Duffin-Kemer-Petiau approach (wave equation) and making a nonrelativistic approximation in the corresponding radial equations, a system of three coupled second order linear differential equations is derived for each type of geometry. For the Minkowski space, the nonrelativistic equations are disconnected using a linear transformation, which makes the mixing matrix diagonal. The resultant three unconnected equatio…
