On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential

TL;DR

This paper revises the understanding of vector couplings in the Duffin-Kemmer-Petiau theory, highlighting differences between minimal and nonminimal potentials, and explores how nonminimal linear potentials can confine bosons without Klein's paradox.

Contribution

It clarifies the behavior of nonminimal vector potentials in DKP theory and demonstrates their role in boson confinement using a mapped harmonic oscillator model.

Findings

Nonminimal vector potentials differ from minimal ones under charge-conjugation and time-reversal.

Nonminimal vector potentials can confine bosons without Klein's paradox.

The DKP equation with linear potentials maps to a harmonic oscillator problem.

Abstract

Vector couplings in the Duffin-Kemmer-Petiau theory are revised. It is shown that minimal and nonminimal vector potentials behave differently under charge-conjugation and time-reversal transformations. In particular, it is shown that nonminimal vector potentials have been erroneously applied to the description of elastic meson-nucleus scatterings and that the space component of the nonminimal vector potential plays a crucial role for the confinement of bosons. The DKP equation with nonminimal vector linear potentials is mapped into the nonrelativistic harmonic oscillator problem and the behavior of the solutions for this sort of DKP oscillator is discussed in detail. Furthermore, the absence of Klein's paradox and the localization of bosons in the presence of nonminimal vector interactions are discussed.