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IEVref:
113-07-17
ID:
Language:
en
Status:
Standard
Term:
four-scalar product
Synonym1:
Minkowski inner product
[
Preferred
]
Synonym2:
Synonym3:
Symbol:
Definition:
real scalar
S
associated with two
four-vectors
x
_
_
and
y
_
_
by the relation
S
2
(
x
_
_
,
y
_
_
)
=
∑
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
Source
Replaces:
Internal notes:
CO remarks:
TC/SC remarks:
VT remarks:
Domain1:
Domain2:
Domain3:
Domain4:
Domain5:
real scalar
S
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4uaaaa@347E@
associated with two
four-vectors
x
_
_
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWG4baaaa aa@34B4@
and
y
_
_
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaWaaWqaaeaacaWG5baaaa aa@34B5@
by the relation
S
2
(
x
_
_
,
y
_
_
)
=
∑
μ
ν
g
μ
ν
x
μ
y
ν
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4uamaaCaaaleqaba GaaGOmaaaakiaacIcadaadbaqaaiaadIhaaaGaaiilamaameaabaGa amyEaaaacaGGPaGaeyypa0ZaaabeaeaacaWGNbWaaWbaaSqabeaaca aH8oGaaqyVdaaakiaadIhadaWgaaWcbaGaaqiVdaqabaGccaWG5bWa aSbaaSqaaiaae27aaeqaaaqaaiaaeY7acaaH9oaabeqdcqGHris5aa aa@4796@
, where
g
μ
ν
MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm 0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9ad baGaaiGaciGacmaaceGaaiGacaabaaGcbaGaam4zamaaCaaaleqaba GaaqiVdiaae27aaaaaaa@374A@
is a component of the
metric tensor
Note 1 to entry: The four–scalar product is a
Lorentz scalar
.