Resonance Interaction Energy in κ‐Minkowski Spacetime

Abstract

If gravity is quantized, one of the consequences may be that the spacetime coordinates are quantized and become noncommutative. The κ‐Minkowski spacetime is such kind of noncommutative spacetime. In this paper, the resonance interaction energy of a two‐atom system coupled with a fluctuating vacuum scalar field in the κ‐Minkowski spacetime is studied. It is found that the resonance interaction energy is dependent on the interatomic separation, the transition wavelength of the atoms, and the spacetime non‐commutativity. When the interatomic separation is small compared with a characteristic length determined by the spacetime non‐commutativity parameter and the transition wavelength, the resonance interaction energy is that in the Minkowski spacetime plus a correction due to the spacetime non‐commutativity. When the interatomic separation is comparable to or larger than the characteristic length, the resonance interaction energy cannot be organized in the form of a Minkowski term plus a correction, which indicates that the long‐range behavior of the vacuum in the κ‐Minkowski spacetime is fundamentally different from that in the Minkowski spacetime.