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The Affine Connexion in Physical Field Theories


1. The loss of connexion by general invariance. The essential physical entities are mathematically described as invariants, vectors, tensors. That comes from the isotropy and homogeneity of space in Euclidean geometry—or from the pseudo-isotropy of space-time, in the Restricted Theory of Relativity. When the latter is replaced by the idea of general invariance, that is, by regarding the three space-co-ordinates and the time only as continuous labels of the world points, which labels may equivalently be replaced by any quadruplet of continuous functions of themselves, the notion of vector, or tensor subsists, but any such entity is now necessarily bound to a given world-point, it is 'a tensor at P'. For example, the displacement-vector, dxk/, leading from a world-point P with co-ordinates xk (that is, x1 x2, x3, x4) to a neighbouring point Q with co-ordinates xk + dxk, is the prototype of a contravariant vector Ak at P. If you change the labels (that is to say, if you execute a general transformation of the frame) the Ak transform by definition as the dxk thus*:

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  1. Einstein, A., Ann. Phys., 49, 769 (1916).

    Article  CAS  Google Scholar 

  2. Weyl, H.,"Raum, Zeit, Materie" (Berlin: Springer; 4th ed., 1918–20); translated by H. L. Brose (London: Methuen, 1922).

    MATH  Google Scholar 

  3. Eddington, A. S., "The Mathematical Theory of Relativity" (Cambridge, University Press, 3rd ed., 1923–30, which includes full reports on Weyl (ref. 2) and Einstein (ref. 4)).

  4. Einstein, A., Site. Ber. d. Preuss. Akad., 32, 76, 137 (1923).

  5. Einstein, A., Site. Ber. d. Preuss. Akad., 414 (1925).

  6. Schroedinger, E., Proc. Roy. Irish Acad., A, 49, 135 (1943).

    Google Scholar 

  7. Schroedinger, E., Proc. Roy. Irish Acad., A, 49, 43 (1943). Three more papers, read to the Royal Irish Academy during 1943, in the Press.

    Google Scholar 

  8. Born, M., Proc. Roy. Soc., A, 143, 410 (1934). Born, M., and Infeld, L., Proc. Roy. Soc., A, 144, 425 (1934). Schroedinger, E., Proc. Roy. Irish Acad., A, 47, 77 (1942); 48, 91 (1942). McConnell, James, Proc. Roy. Irish Acad., A, 49, 149 (1943).

    Article  ADS  Google Scholar 

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SCHROEDINGER, E. The Affine Connexion in Physical Field Theories. Nature 153, 572–575 (1944).

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