A Unified Metric

Abstract

A new operation which can act on the combined tensor products of the tangent and the cotangent spaces at a point of a differentiable manifold is presented. It is demonstrated that, under the operation, when a self-product of a unit tensor acts on a pair of vectors, the Clifford structure arises without matrices. In conjunction with a unit tensor, the new operation is also shown to naturally transform vectors to forms. The new product is associative when applied to unit tensors but not generally otherwise.