GEOMETRIC GAUGE UNIFICATION OF THE FOUR FUNDAMENTAL INTERACTIONS OF ELEMENTARY PARTICLES.

摘要

A high-dimensional unified field theory of all fundamental forces between elementary particles is formulated with emphasis on the gauge theoretic treatment of gravitation.; Firstly, the de Sitter gauge theory of gravitation is incorporated into the Kaluza-Klein scheme. The global SO(4,1) symmetry requirement leads to a uniformly curved spacetime, whereas the localization of the symmetry results in a generally curved ten-dimensional geometry. Gravitation is then described by the gauge fields A(,(mu))('a) as well as the metric fields g(,(mu)(nu)). The dual description of the gravitational fields is essential in casting the gauge theory of gravitation into the Kaluza-Klein scheme. On the other hand, this formulation brings about the Yang term as a source to Einstein's field equation. A test particle placed in this gravitational geometry is found not to follow a geodesic path in spacetime. This dilemma may be resolved by requiring that the gravitational charge, an analogue of the electric charge, carried by the particle is always zero. In fact, with this requirement and a built-in constraint in the 10-dimensional geometry, the contribution from the Yang term vanishes identically. Therefore, the Kaluza-Klein scheme formulated for pure gravitation is equivalent to Einstein's general relativity, though the presence of the cosmological term is necessary in order to assure the global SO(4,1) symmetry as a limit. The present formulation of gravitation, even if equivalent to Einstein's theory, has an advantage that it provides a framework for the unification with gravitation at equal footing with the other fundamental forces.; Thus, secondly, a unified treatment of all fundamental forces is developed by extending the Kaluza-Klein scheme to a (10 + n)-dimensional scheme. Upon localization of the de Sitter symmetry, the Lorentz group SO(3,1) has locally been preserved. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of school.) UMI