4 1 2 D O C . 4 5 9 F I E L D T H E O R Y & H A M I LT O N P R I N C I P L E By computation, we find ,[9] (11a) where , (13) is, a quantity that is antisymmetric in all three indices. By carrying out the variation of H and separating the resulting tensor equation into symmetric and antisymmetric parts, one obtains in addition to (9) also the equations . (14) Here, σ denotes the ratio of the infinitesimal quantities ε 2 and ε 1 . These equations can also be written in the form . (14a) By computation, one arrives at (15) (16) and, after carrying out the operation /ν from (14a), , (17) or, after introducing the contravariant tensor density , . (17a) One can see immediately that these equations contain the Maxwell theory to first approximation. For in the first place, the dependence of the “field strengths” f  on the “potentials”  μ are to first order the same as in Maxwell's theory. In the second place, since the symbol /ν indicates ordinary differentiation in the first approxima- tion—differentiation with respect to α will lead to the vanishing of f μα / , due to the antisymmetry of S. However, in order to do justice to the existence of electric charges, we shall have to consider the limiting case of σ = 0. H * 1 12 - hS   S   – = [p. 158] S            + + = G * G * –    G ** G ** –   + 0 = H  * H  * –   /  H  ** H  ** –   / + 0 = H  * H  * – h – S   S –   = = H  ** H  ** – h   g    g  –   = S /   h       –  – 0 = f S /  f  – 0 =