density of weight +1. It is often written as or where and the differential form are absolute tensors, and where is the Levi-Civita symbol; see below. The density of Lorentz force (that is, the linear momentum transferred from the electromagnetic field to matter within a 4-volume element divided by that element — do not use the metric in this calculation) is a covariant vector density of weight +1. In N-dimensional space-time, the Levi-Civita symbol may be regarded as either a rank-N covariant (odd) authentic tensor density of weight −1 () or a rank-N contravariant (odd) authentic tensor density of weight +1 (). Notice that the Levi-Civita symbol (so regarded) does obey the usual convention for raising or lowering of indices with the metric tensor. That is, it is true that but in general relativity, where is always negative, this is never equal to The determinant of the metric tensor, is an (even) authentic scalar density of weight +2, being the contraction of the product of 2 (odd) authentic tensor densities of weight +1 and four (even) authentic tensor densities of weight 0. See also Notes References . . Differential geometry Tensors Tensors in general relativity