3 4 2 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 365.“On Unified Field Theory” [Einstein 1929n] Dated 1929 Presented 10 January 1929 Published 30 January 1929 IN: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse. Sitzungsberichte (1929): 2–7. In two recently published papers1 I have attempted to show that one could arrive at a unified theory of gravitation and electricity by attributing to the four- dimensional continuum, in addition to a Riemannian metric, also the property of “distant parallelism.” Indeed, it proved possible to give a unified interpretation to the gravitational field and the electromagnetic field. However, the derivation of the field equations from the Hamiltonian principle did not lead to a simple and com- pletely unique method. These difficulties increased on more careful consideration. In the meantime, however, I have succeeded in finding a satisfactory[2] method for the derivation of the field equations, which I shall disclose in the following. § 1. Formal Preliminaries I will make use of the notation that was recently suggested by Mr. Weitzenböck[3] in his work on this subject.2 The ν-th component of the s-th axis of the n-Bein frame (coordinate system) will be denoted by s , and s h ν will denote the corresponding normalized subdeterminants. The local n-Bein frames are all placed “parallel.” Parallel and equal vectors are those that have the same coordi- nates with respect to their local n-Bein frame. The parallel displacement of a vector is given by the formula , [5] where the comma in s h α,β indicates that the derivative with respect to x β is to be computed in the ordinary manner. The “Riemannian curvature tensor” formed from the Δμ αβ (which are not symmetric in α and β) vanishes identically. 1 These Berichte VIII, 28 and XVII, 28.[1] 2 These Berichte XXVI, 28.[4] [p. 2] A  A x – h s A x –sh = =
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