A Five Dimensional Unification of the Poincare Gauge and Electromagnetic Fields

概要

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A Kaluza-Klein type unification of the Poincare gauge and electromagnetic fields is developed on the basis of the principal fiber bundle over the four dimensional space-time with the group U(1). The vierbein, Lorentz gauge and electromagnetic fields are unified into the funfbein and de Sitter gauge fields on the bundle space. The most general Lagrangian densities of the funfbein fields and of the Sitter gauge fields, which are functions of these fields and of their first derivatives and are at most quadratic in the derivatives, are given. They have eleven parameters in addition to the "radius" r of the fifth dimensional side of the bundle space. Restrictions imposed on these parameters from physical requirements are given, a part of which agrees with one of the conditions which Hayashi and Shirafuji arrived at in Poincare gauge theory of gravitation. A five dimensional Lagrangian density which leads to the Dirac equation of four dimensional spinor field is given. Any Dirac field defined as a pullback of the spinor field on the bundle space is expected to have an electric dipole moment with the magnitude √<hc>|r|/4. The geometric structure with regard to affine connections is discussed also.
理論物理学刊行会の論文
1983-04-25