D O C U M E N T 4 8 0 K A L U Z A’ S T H E O R Y: PA R T 2 4 7 7 . (9a) The raising of the indices should be understood with respect to the metric in R4. For the calculation of H, the following further equations are necessary (Roman letters run from 1 to 4 ): (18) where . (19) From (18) and (9a), one obtains the – Γ in the form . (20) γα g11 g22 . –φ1 g12 g22 . . –φ2 . . . . . . . . . . –φ1 φ2 – . . 1 φaφa + = gmndxmdxn [p. 29] m n s m n s φsψmn φmφsn φnφsm + + + = 0 n s φsn = m n 0 ψmn = 0 0 s 0 n 0 0 0 0 0 = = = ψmn 1§ 2© -- - ∂xn ∂φm ∂xm¹ ∂φn + ¨ ¸ · = φmn 1§ 2© -- - ∂xn ∂φm ∂xm¹ ∂φn – ¨ ¸ · = Γmn s Γmn s φmφn s φnφms + + = Γmn s φsΓmn s – φs( φmφsn φnφsm) + – = Γ0n s φn s = Γ0 0n φsφsn –= Γ00 s Γ0 00 0 = =