D O C U M E N T 3 6 5 O N U N I F I E D F I E L D T H E O R Y 3 4 3 As “covariant differentiation,” we use only those differential quotients formed by using the Δ. Following the convention of the Italian mathematicians, we denote it by a semicolon,[6] thus , . Since the s h ν and the g μν ( ) as well as the gμν have vanishing covariant de- rivatives, these quantities can be commuted at will as factors with the covariant dif- ferentiation symbol.[7] Here, I deviate from the usual notation by defining the tensor Λ (and leaving off the factor 1/2)[8] as follows: . The principal difference with respect to the usual formulas of absolute differen- tial calculus, which is accompanied by the introduction of a nonsymmetric dis- placement law, is found in the definition of the divergence. Let T:: σ be some arbitrary tensor with the upper index σ. Its covariant derivative, if we write only the extension term with regard to the index σ, is given by . [9] Multiplying this equation by the determinant h, after contracting it with respect to σ and τ, and introducing the tensor density T on the right-hand side, one then ob- tains . [10] The last term on the right-hand side would vanish if the displacement law were symmetric. It is itself a tensor density, like all of the other terms on the right-hand side together, which we term the divergence of the tensor density T, in agreement with the conventional notation, and for which we will write . One then obtains . [11] (1) Finally we wish to introduce a notation that, as it seems to me, improves the clarity of the theory. On occasion, I will indicate raising or lowering of an index by under- lining the corresponding index. For example, I will denote the pure contravariant tensor belonging to (Λ μν ) by (Λ μν ), and the corresponding pure covariant tensor by (Λ μν ).[12] A A , A – A A , A + h s h s [p. 3] – T:: x T . . . . T:: + + hT:: x T:: T:: + + T. . / . . hT:: T::/ T:: +