Duffin–Kemmer–Petiau theory with minimal and non-minimal couplings

Abstract

In this work we study the properties of the Duffin–Kemmer–Petiau (DKP) formalism in a general representation of β matrices. In particular, we analyze the conservation of the total angular momentum, and the effects of minimal and non-minimal prescriptions. The selection of the scalar and vector sectors of the formalism is done in a simple and consistent way by using operators independent of a specific choice of representation. Physical applications are explored, in which the minimal prescription reproduces the system in the presence of external magnetic field, and the non-minimal one leads to the DKP oscillator. We obtain and discuss the motion equations, eigenstates and energy spectrum of the different sectors of the theory for the two types of couplings.