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Darstellungsformeln erster Näherung für G REEN sche Funktionen von Wellengleichungen in R IEMANN scher Raum‐Zeit
Author(s) -
John R. W.
Publication year - 1974
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19740600111
Subject(s) - mathematics , scalar (mathematics) , mathematical physics , real line , perturbation (astronomy) , mathematical analysis , combinatorics , geometry , physics , quantum mechanics
By applying perturbation theory to the construction scheme for G REEN 's functions in a curved R IEMANN ian space‐time due to H ADAMARD , explicit formulae for scalar and vector G REEN 's functions in the first post‐M INKOWSKI an approximation are derived. The two‐point functions entering into the construction are represented by integrals of the first‐order metric terms and their derivatives taken along the straight line joining the two points. Using these expressions, one obtains explicit conditions for the validity of H UYGEN 's principle for the wave equations in the first approximation.