Effects Due to a Scalar Coupling on the Particle-Antiparticle Production in the Duffin-Kemmer-Petiau Theory

Abstract

The Duffin-Kemmer-Petiau formalism with vector and scalar potentials is used to point out a few misconceptions diffused in the literature. It is explicitly shown that the scalar coupling makes the DKP formalism not equivalent to the Klein-Gordon formalism or to the Proca formalism, and that the spin-1 sector of the DKP theory looks formally like the spin-0 sector. With proper boundary conditions, scattering of massive bosons in an arbitrary mixed vector-scalar square step potential is explored in a simple way and effects due to the scalar coupling on the particle-antiparticle production and localization of bosons are analyzed in some detail.

Remarks on the Spin-One Duffin-Kemmer-Petiau Equation in the Presence of Nonminimal Vector Interactions in(3+1)Dimensions

“…where the adjoint spinor ψ is given by ψ = ψ † η 0 with η 0 = 2β 0 β 0 − 1 in such a way that (η 0 β µ ) † = η 0 β µ (the matrices β µ are Hermitian with respect to η 0 ). Despite the similarity to the Dirac equation, the DKP equation involves singular matrices, the time component of J µ is not positive definite and the case of massless bosons cannot be obtained by a limiting process [52]. Nevertheless, the matrices β µ plus the unit operator generate a ring consistent with integer-spin algebra and J 0 may be interpreted as a charge density.…”

Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in(1+1)-dimensions with a scalar linear potential

“…Comparison of ( 11) with (15) evidences that the spinors Ψ I , Ψ II and Ψ III behave like the spinor components Ψ 1 , Ψ 2 and Ψ 3 , respectively, from the spin-0 sector of the DKP theory. More than this, comparison of ( 12) with ( 16) places on view that the spin-1 sector of the DKP theory looks formally like the spin-0 sector [12]. For a time-independent scalar potential, one can write Ψ(x, t) = ψ(x) exp(−iEt).…”

“…Due to weak potentials, relativistic effects are considered to be small in solid state physics, but the relativistic wave equations can give relativistic corrections to the results obtained from the nonrelativistic wave equation, therefore the relativistic extension of this problem is also of interest and remains unexplored. The scalar interaction in the context of the DKP theory has been reported in the literature for a smooth step potential [11], step potential [12],…”

The superradiance phenomenon in spin-one particles

“…In contrast to the Dirac equation, the DKP equation describes vector (spin-one), and scalar (spin-zero) particles 3 . Remarkably, when the DKP equation is under the influence of a one-dimensional potential, the formalism for the spin-one is similar to the spin-zero formalism 4 .…”