Dirac field in the five-dimensional Kaluza-Klein theory

The authors consider the five-dimensional Kaluza-Klein theory with a Dirac field coupled to the metric field. As a result, the authors obtain a four-dimensional Einstein-Maxwell-Dirac theory with an extra CP violating term. The resultant anomalous electromagnetic dipole moment of the electron is of the order of magnitude of about 10^-31 e cm, and may not be detectable by present experimental techniques. However, the mass of the charged Dirac particle is found to be of the order of the Planck mass (10^-7 g), so that the Kaluza-Klein theory containing spin-1/2 particles must be rejected.