Hy. Liu et Ps. Wesson, PARTICLE MASSES IN KALUZA-KLEIN-GORDON THEORY AND THE REALITY OF EXTRA DIMENSIONS, Modern physics letters A, 13(33), 1998, pp. 2689-2694
To see how the effective 4-D mass of a particle is affected by the geo
metry of an ND space, we take the Klein-Gordon equation in 5-D and eva
luate it in PD using two exact solutions of 5-D Kaluza-Klein theory. T
he mass (squared) turns out to be complex if the theory is independent
of the extra coordinate, but can be made real if the wave function de
pends on an extra dimension which is physical. These results have sign
ificant implications for 10-D superstring theory.