D O C U M E N T 1 4 6 C A L C U L A T I O N S 2 5 5 146. Calculations [Berlin, ca. January–February? 1926][1] soll erfüllt sein bei jeder Wahl der Differentiale ____________________________________________________________ [2] AD. [17 268.1], [28 041.1]. Written on the verso of the drafts of Abs. 258 and Doc. 193. [1]Dated from Abs. 258 and Doc. 193. [2]This is a so-called Weyl connection as used in Weyl’s unified field theory. For details see Vol. 8, Doc. 472, note 3 and Goenner 2004, sec. 4.1. δ( gμνAμAν) 0 wenn gμνAμAν 0 = = gμν 1= δAμ Γαβ μ Aαδxβ –= β μ ∂xα ∂gμν δxαAμAν 2 A²gμνAνΓαβ ¢ β μ Aαδxβ – 0 wenn gμνAμAν 0 = = μα α gδiklmdxidykdzldum) Δ( 0 Bedingung für die Mannigf. = β i ∂ g ∂xα ----------δiklmdxidykdzldumδξαα² ¢ gδiklmdykdzldum( i dxβδξα) –Γβα • + + β i ∂lg g ∂xα --------------- α δ²δiklm( –Γiβ ¢ α –δβklmΓiβ ) • – • – © ¹ § · dxidykdzldumδξα 0= ( ) 0= i k l m 1 2 3 4 ∂lg g ∂xα --------------- Γ1α 1 – Γ2α 2 – Γ3α 3 – Γ4α 4 – 0 = ∂xα ∂gμν gβνΓμα β – gμβΓνα β – λαgμν + 0 = Γμα ν ∂ ∂xα ----------g = Γμν α gαβ μ ν β 1 2 -- - gμβλν gνβλμ gμνλβ) –+ ( + = ausserdem ist gαβ§ 1 2 --²gμβλα - ¢ gαβλμ gμαλβ¹ –+ © · 0= λμ 4λμ λμ – + 0. =