IEC 60050 - International Electrotechnical Vocabulary


IEVref:	113-07-54		ID:
Language:	en		Status: Standard

Term:	stress-energy tensor
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Symbol:	$T$
Definition:	symmetric 4 × 4 tensor that provides the flux of the $μ^{th}$ component of the four-momentum $\underline{\underline{p}}$ across a surface in space-time with constant component $x_{ν}$ by $T_{μ ν} : = \frac{1}{μ_{0}} (\sum_{κ} F_{μ κ} F_{κ ν} + \frac{1}{4} δ_{μ ν} \sum_{κ λ} F_{κ λ}^{2})$ , where $μ_{0}$ is magnetic constant, $F_{μ ν}$ are components of the electromagnetic field tensor, and $δ_{μ ν}$ is Kronecker symbol Note 1 to entry: The coherent SI unit of the stress-energy tensor is kilogram metre per second, $kg \cdot m \cdot s^{-1} = J \cdot m^{−3}$ .
Publication date:	2022-06
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μ th MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaqiVdmaaCaaaleqaba GaamiDaiaadIgaaaaaaa@36FE@ four-momentum p _ _ MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaameaabaGaam iCaaaaaaa@36F1@ space-time x ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamiEamaaBaaaleaaca aH9oaabeaaaaa@3615@ T μν := 1 μ 0 ( ∑ κ F μκ F κν + 1 4 δ μν ∑ κλ F κλ 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamivamaaBaaaleaaca aH8oGaaqyVdaqabaGccaqG6aGaeyypa0ZaaSaaaeaacaaIXaaabaGa aqiVdmaaBaaaleaacaaIWaaabeaaaaGcdaqadaqaamaaqafabaGaam OramaaBaaaleaacaaH8oGaaqOUdaqabaGccaWGgbWaaSbaaSqaaiaa eQ7acaaH9oaabeaakiabgUcaRmaalaaabaGaaGymaaqaaiaaisdaaa GaaqiTdmaaBaaaleaacaaH8oGaaqyVdaqabaGcdaaeqbqaaiaadAea daqhaaWcbaGaaqOUdiaaeU7aaeaacaaIYaaaaaqaaiaaeQ7acaaH7o aabeqdcqGHris5aaWcbaGaaqOUdaqab0GaeyyeIuoaaOGaayjkaiaa wMcaaaaa@5752@ μ 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaqiVdmaaBaaaleaaca aIWaaabeaaaaa@35D1@ magnetic constant F μν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaamOramaaBaaaleaaca aH8oGaaqyVdaqabaaaaa@3728@ electromagnetic field tensor δ μν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaaqiTdmaaBaaaleaaca aH8oGaaqyVdaqabaaaaa@379A@ Kronecker symbolNote 1 to entry: The coherent SI unit of the stress-energy tensor is kilogram metre per second,

kg \cdot m \cdot s^{-1} = J \cdot m^{−3}

.