Quantum dynamics of particles in a discrete two-branes world model: Can matter particles exchange occur between branes?

In a recent paper, a model for describing the quantum dynamics of massive particles in a non-commutative two-sheeted spacetime was proposed. This model considers a universe made with two spacetime sheets embedded in a 5D bulk where the fifth dimension is restricted to only two points. It was shown that this construction has several important consequences for the quantum dynamics of massive particles. Most notably, it was demonstrated that a coupling arises between the two sheets allowing matter exchange in presence of intense magnetic vector potentials. In this paper, we show that non-commutative geometry is not absolutely necessary to obtain such a result since a more traditional approach allows one to reach a similar conclusion. The fact that two different approaches provide similar results suggests that standard matter exchange between branes might finally occur contrary to conventional belief.