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Dirac equation in a 5-dimensional Kaluza-Klein theory

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  • M. Ansari

    (North-Eastern Hill University)

Abstract

Dirac equation is discussed in 5-dimensional space time having topology M 4 ×T 1, whereM 4 and T 1 both are curved. It is shown that 4-dimensional fermion can be obtained from 5-dimensional fermion, as a result of compactification of 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. 4-dimensional Dirac equation, obtained from 5-dimensional Dirac equation after compactification, is solved for an arbitrary mode for superheavy as well as light (realistic) fermions. Time-dependence of polarization vector and magnetization density, as a result of Gordon-decomposition of the current vector for 4-dimensional spin-½ field (with arbitrary mode), is exhibited.

Suggested Citation

  • M. Ansari, 2010. "Dirac equation in a 5-dimensional Kaluza-Klein theory," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(6), pages 715-736, December.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:6:d:10.1007_s13226-010-0041-x
    DOI: 10.1007/s13226-010-0041-x
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