(Received May 11, 1976)
Dirac equation is generalized in a way that combines the mass term with the term describing interaction with the gravitational field. The new equation is de Sitter invariant and involves covariant derivatives of the Dirac wave function in a fibre bundle associated with a principal fibre bundle which has a five-dimensional base manifold and de Sitter structure group. Such a principal fibre bundle may be reduced to the bundle of linear frames of a four-dimensional manifold when a specific cross-section is chosen. The generalized Dirac equation reduces then to the ordinary one with the mass term generated by the translational part of the covariant derivative. In such a way analogy between charge and mass is obtained. Every cross-section has its conjugate with reversed vertical components of all tangent vectors. It gives a geometrical meaning to charge conjugation.
URL : http://ptp.ipap.jp/link?PTP/57/1771/
DOI : 10.1143/PTP.57.1771