D O C . 5 2 O N T H E A F F I N E F I E L D T H E O R Y 8 9
Published in Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse.
Sitzungsberichte (123): 137–140. Presented 31 May 1923, published 28 June 1923. A manuscript
[1 034] is also available. It consists of five pages, the first three of which are in Paul Ehrenfest’s hand
(except for one line at the bottom of the second page). The bottom parts of both the third and the fourth
page were cut off; on each of these pages, two crossed-out lines of text are still visible.
The earlier papers mentioned are Einstein 1923e (Vol. 13, Doc. 425) and Einstein 1923h
Johannes Droste (1886–1963), Professor of Mathematics at the University of Leyden. The sec-
ond sentence of the footnote is missing in the manuscript. In a letter to Einstein dated 27 March 1943,
Erwin Schrödinger wrote about work of his own along similar lines, and that the first sentence of the
footnote is in error, since the function remains “in principle” a function of the 16 affine (see
[22 066] and Schrödinger 1943).
The assumption referred to in this footnote was employed in Einstein 1923e (Vol. 13, Doc. 425).
See eq. (17) of Einstein 1923e (Vol. 13, Doc. 425).
The words “zur Feldstärke der Feldtensor bzw. der kovariante .” were added in
Einstein’s hand in the manuscript.
This result corresponds to eq. (4) of Einstein 1923h (Doc. 13).
After eq. (9), the manuscript continues: “Unsere nächste Aufgabe besteht in der Wahl der Hamil-
ton’schen Funktion . Es sei zunächst.” The remainder of the page was cut off, and the manuscript
continues with the next page, which is in Einstein’s hand.
These field equations are to be compared with eq. (13) of Einstein 1923h (Doc. 13).
After the sentence ending with “Theorie,” the manuscript begins with a new paragraph that
reads: “Zunächst könnte man glauben, dass die Gleichung.” The new paragraph, however, was
crossed out, the remainder of the page was cut off, and the manuscript continues on the next page. On
that manuscript page, the factor β in eqs. (11a), (13), (15), (16) and in the last paragraph was corrected
from a factor together with some corrected signs.
The manuscript ends with the words, “Dann müssen bei endlichen und elektrischen Feldern.”
For further historical discussion of the affine field theory approach, see Stachel 1986; Vizgin 1994,
pp. 188–197; Goenner 2004, sec. 4.3; Sauer and Majer 2005; Sauer 2014a.