The Vector Boson Oscillator in Doubly Special Relativity

Abstract

We derive a relativistic wave equation for spin-1 vector bosons within the framework of Amelino-Camelia's doubly special relativity (DSR). By implementing non-minimal substitutions, we obtain a DSR-modified two-dimensional vector boson oscillator equation, formulated in terms of a symmetric rank-two spinor. This leads to a coupled system of first-order equations, including one algebraic equation, that governs the dynamics of the modified spin-1 vector boson oscillators. From this system, we extract an exactly solvable wave equation that incorporates first-order DSR corrections. The solutions are expressed in terms of special functions, and we present a closed-form expression for the energy spectrum, which explicitly incorporates the effects of DSR. Remarkably, our results reveal mass splittings induced by DSR between spin-1 oscillator and anti-oscillator modes. Furthermore, we show that these modes manifest exclusively as rotating, ring-shaped structures. The analysis is general and applies to both the low-energy regime and the non-relativistic limit.