Dirac equation in a 5-dimensional Kaluza-Klein theory (Q550685)

The Dirac equation is discussed in 5-dimensional space time having topology \(M(4)\times T(1)\), where \(M(4)\) and \(T(1)\) both are curved. It is shown that the 4-dimensional fermion can be obtained from the 5-dimensional fermion, as a result of a compactification of the extra dimension. It is found that the realistic 4-dimensional fermions are possible in higher modes earlier than those in lower modes during the course of expansion of 4-dimensional universe. The 4-dimensional Dirac equation, obtained from the 5-dimensional Dirac equation after compactification, is solved for an arbitrary mode for superheavy as well as light (realistic) fermions. Time-dependence of the polarization vector and magnetization density, as a result of a Gordon-decomposition of the current vector for the 4-dimensional spin-\(\frac12\) field (with arbitrary mode), is exhibited.