IEVref:113-07-42ID:
Language:enStatus: Standard
Term: four-nabla
Synonym1: quabla
[Preferred]
Synonym2: diamond
[Preferred]
Synonym3:
Symbol: ◊ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaeyiXIaoaaa@35F8@ (Unicode: U+25CA)
Definition: four-dimensional generalization of three-dimensional nabla operator ∇ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaey4bIenaaa@352C@ given by the four-vector

◊=( ∂ ∂ x 0 , ∂ ∂ x 1 ,  ∂ ∂ x 2 ,  ∂ ∂ x 3 )=( ∂ ∂j c 0 t ;∇ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaeyiXIaUaeyypa0Zaae WaaeaadaWcaaqaaiabgkGi2cqaaiabgkGi2kaadIhadaWgaaWcbaGa aGimaaqabaaaaOGaaiilamaalaaabaGaeyOaIylabaGaeyOaIyRaam iEamaaBaaaleaacaaIXaaabeaaaaGccaGGSaGaaGjbVpaalaaabaGa eyOaIylabaGaeyOaIyRaamiEamaaBaaaleaacaaIYaaabeaaaaGcca GGSaGaaGjbVpaalaaabaGaeyOaIylabaGaeyOaIyRaamiEamaaBaaa leaacaaIZaaabeaaaaaakiaawIcacaGLPaaacqGH9aqpdaqadaqaam aalaaabaGaeyOaIylabaGaeyOaIyRaaeOAaiaadogadaWgaaWcbaGa aGimaaqabaGccaWG0baaaiaacUdacqGHhis0aiaawIcacaGLPaaaaa a@5C49@

Note 1 to entry: Four-nabla is useful in STR. In general theory of relativity (GTR) for non-flat space-time, a more sophisticated method is used.

Note 2 to entry: In the International System of Quantities, the dimension of four-nabla is L −1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGabaqaamaaceGaaiGacaabaaGcbaGaciitamaaCaaaleqaba GaeyOeI0IaaGymaaaaaaa@35AD@ .


Publication date:2022-06
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