albivaldmaple

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restart; with(Physics)

Physics:-Setup(spacetimeindices)

[spacetimeindices = greek]

(1)

Physics:-Setup(mathematicalnotation = true);

[mathematicalnotation = true]

(2)

Physics:-Setup(signature = "-+++")

[signature = `- + + +`]

(3)

macro(LM = `𝕃`, %LM = `%𝕃`):

LM[`~mu`, nu] = Matrix(4, symbol = L)

`𝕃`[`~mu`, nu] = Matrix(%id = 18446746054088983006)

(4)

Physics:-Define(`𝕃`[`~mu`, nu] = Matrix(%id = 18446746054088983006))

{Lambda, `𝕃`[`~mu`, nu], Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu]}

(5)

NULL

L[1, 1] := 1:``

L[2, 1] := 0:

L[3, 1] := 0:

L[4, 1] := 0:

``

``

Physics:-Library:-TensorComponents(LM[`~mu`, nu])

[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, cos(varphi), -sin(varphi), 0, 0, sin(varphi), cos(varphi)]

(6)

TensorArray(LM[`~mu`, nu])

Matrix(%id = 18446746054088934694)

(7)

g_[]

g[mu, nu] = (Matrix(4, 4, {(1, 1) = -1, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 2) = 1, (2, 3) = 0, (2, 4) = 0, (3, 3) = 1, (3, 4) = 0, (4, 4) = 1}, storage = triangular[upper], shape = [symmetric]))

(8)

NULL

Physics:-`*`(Physics:-`*`(Physics:-g_[mu, nu], LM[`~mu`, rho]), LM[`~nu`, sigma])

Physics:-g_[mu, nu]*`𝕃`[`~mu`, rho]*`𝕃`[`~nu`, sigma]

(9)

Physics:-Simplify(Physics:-g_[mu, nu]*`𝕃`[`~mu`, rho]*`𝕃`[`~nu`, sigma])

`𝕃`[nu, sigma]*`𝕃`[`~nu`, rho]

(10)

``

Download Verify_lorentz_transformation.mw

Hello Edgardo , thank's for answering me

I did that . ( see attachment) 

1) Define a lorentz transformation - Axis rotation ( It conserves MInkowski)

2) Calculate 

I would expect this result . 

Instead I see

He lowered index in the first product.

Best regards

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