Five-dimensional Kaluza-Klein Theory reformulated

Abstract

This paper presents a reformulation of the five-dimensional Kaluza-Klein theory. taking into consideration the fact that these five dimensions of space-time are present on the tangent bundle of the Principal Bundle (B). Tb1s reformulation is possible due to the group U(l) of the fiber which endows B with the structure of a differential manifold. this allowing the reproduction of parallel transport notions on such a manifold. Through this we achieve a criterion to add extra dimensions to the theory. Once this criterion has been established. a metric ís constructed on the tangent bundle of B. which is formed by a metric of space-time plus a connection, the a one-form defined in the fiber of B whose curvature 1s proportional to the electromagnetic field. This. the five-dimensional Einstein action is the sum of the four-dimensional Einstein action and the four-dimensional Maxwell action. This formulation yields the Einstein and Maxwell equations, as well as the Yang-Mills equations.

Keywords

• fiber bundles
• Kaluza-Klein theory