ABSTRACT

One of the central problems faced by theoretical physics is to explain the nature and origin of the forces that act between fundamental particles. In the case of gravity, this is elegantly achieved (at the non-quantum-mechanical level) by general relativity. With hindsight, we may say that an explanation of gravitational forces arises naturally-indeed, almost inevitably-from a systematic and explicit account of the geometrical structure of spacetime. The origin of gravitational forces, as described in chapter 4, may be summarized as follows:

(i) To relate physical quantities (represented by tensors) at different points of spacetime, we must introduce a specific geometrical structure, the affine connection, which defines parallel transport.