5-Dimensional Spacetime with q-Deformed Extra Dimension

An attempt to obtain the non-trivial mass structure of particles in a Randall-Sundrum type of 5-dimensional spacetime with a q-deformed extra dimension is discussed. In this spacetime, the five-dimensional space has no boundary, but there arises an elastic potential preventing free motion in the fifth direction. The q-deformation is, then, introduced in such a manner that a non-commutativity arises in the spacetime coordinates between the 4-dimensional components and the fifth component. As a result of this q-deformation, the propagators of particles embedded in this spacetime naturally acquire an ultraviolet-cutoff effect without spoiling the Lorentz covariance in the 4-dimensional spacetime.