IEC 60050 - International Electrotechnical Vocabulary


IEVref:	113-07-17		ID:
Language:	en		Status: Standard

Term:	four-scalar product
Synonym1:	Minkowski inner product [Preferred]
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Definition:	real scalar $S$ associated with two four-vectors $\underline{\underline{x}}$ and $\underline{\underline{y}}$ by the relation $S^{2} (\underline{\underline{x}}, \underline{\underline{y}}) = \sum_{μ ν} g^{μ ν} x_{μ} y_{ν}$ , where $g^{μ ν}$ is a component of the metric tensor Note 1 to entry: The four–scalar product is a Lorentz scalar.
Publication date:	2022-06
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S MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4uaaaa@347E@ four-vectors x _ _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWG4baaaa aa@34B4@ y _ _ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWG5baaaa aa@34B5@ S 2 ( x _ _ , y _ _ )= ∑ μν g μν x μ y ν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4uamaaCaaaleqaba GaaGOmaaaakiaacIcadaadbaqaaiaadIhaaaGaaiilamaameaabaGa amyEaaaacaGGPaGaeyypa0ZaaabeaeaacaWGNbWaaWbaaSqabeaaca aH8oGaaqyVdaaakiaadIhadaWgaaWcbaGaaqiVdaqabaGccaWG5bWa aSbaaSqaaiaae27aaeqaaaqaaiaaeY7acaaH9oaabeqdcqGHris5aa aa@4796@ g μν MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4zamaaCaaaleqaba GaaqiVdiaae27aaaaaaa@374A@ metric tensorNote 1 to entry: The four–scalar product is a Lorentz scalar.