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Die E INSTEIN ‐Gruppe und die Symmetrie‐Gruppen der Gravitationstheorie
Author(s) -
Treder H.J.
Publication year - 1973
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19734830406
Subject(s) - hypersurface , physics , covariant transformation , space (punctuation) , mathematical physics , einstein , function (biology) , group (periodic table) , phase space , combinatorics , pure mathematics , mathematics , quantum mechanics , computer science , evolutionary biology , biology , operating system
The transformations x −α = x −α ( x β , g μn̈ ) in the function space of the g μn̈ ( x λ ) are corresponding to the coordinate transformations x α = x α ( x β ) with some non‐covariant conditions on the g μn̈ ( x λ ). Therefore, the transformations in the function space are corresponding to subgroups of the E INSTEIN group. The conditions for the g μn̈ may be given in the space‐ time V 4 or on submanifolds (points, curves, surfaces and hypersurfaces) of the V 4 . – A special case of the last problem is given by the C AUCHY conditions or by the D IRAC constraints for a special choice of the coordinates on a C AUCHY hypersurface x 0 = 0. Then, the transformations x −α = x −α ( x l , g rs , p mn ) in the phase space are E INSTEIN transformations preserving the synchronicity for x 0 → 0.