D O C U M E N T 4 1 8 C A L C U L A T I O N S I N D I A R Y 6 9 3 [40]The right-hand side should read . [41]The first term should have a factor ½, the fifth should have a factor –2, and the sixth term should have a factor –½. The final result, , is not affected by these algebraic mistakes. [42]The last term should be . [43]At this point, Einstein explicitly started to proceed along the assumptions of the published ver- sion, Einstein 1923e (Doc. 425). The Hamiltonian is assumed to depend on the connection, in such a way that it depends only on the symmetric part, i.e., a symmetric, covariant metric field , and the antisymmetric part, i.e., an antisymmetric, covariant electromagnetic tensor field the corre- sponding contravariant tensor densities and are defined by variation of H with respect to and , respectively. Field equations, however, are obtained by variation only with respect to the connection . [44]Compare this equation with eq. (13) of Einstein 1923e (Doc. 425). [45]Einstein implicitly introduces a notation by which an overbar denotes symmetrization, e.g., . [46]The factor ½ appears to have been inserted as an afterthought. The brackets should be around . At this point, in the corresponding equation of Einstein 1923e (Doc. 425 compare its eqs. (6) and (12)), Einstein introduced a scale factor λ. [47]If Einstein had defined above with a factor ½ (see the preceding note), the factors of 2 in front of the term in this line, as well as in front of the similar term in the line above, should be factors of 1. [48]Einstein introduces a covariant derivative of the symmetric tensor density compare eq. (16) of Einstein 1923e (Doc. 425). There should be an equal sign after . [49]If Einstein had defined above with a factor ½ (see note 46 above), the last two terms would carry factors of ½ see also eqs. (14) and (17) of Einstein 1923e (Doc. 425). In going to the next line, Einstein contracts [eq. 16] with and defines the quantities and (see note 27 above). [50]The last equation should read . [51]The second and third terms should have a factor of 20/3 instead of 3/20 (see the preceding note). The last two terms would carry factors of ½ if Einstein had defined above with a factor ½ (see note 46 above). [52]Einstein apparently goes back to [eq. 16] on the preceding page. The second term should be . 3 2 --Eσ - – Dσ – E D0 = = 3 2 --Dσ - gμν ϕμν gμν fμν gμν ϕμν Γμν α α ∂Γμα ∂xν ------------ 1 2 -- - α ∂Γμα ∂xν ------------ α ∂Γνα ∂xμ ------------ + ≡ α ∂Γμα ∂xν ------------ α ∂Γνα ∂xμ ------------ – ϕμν ∂fμβ ∂xβ ----------δα ν gμν α ϕμν δν α Dμ gμν α ≡ iμ ∂fμβ ∂xβ ---------- ≡ Dμ 10 3 -----iμ - –= ϕμν ∂gμβ ∂xβ -----------δα ν