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edited Aug 21 at 13:25

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I have the following vectors:

    p3 = {Subscript[m, \[Tau]]τ]/\[Sqrt]√(1 - \[Beta]^2β^2), (   Subscript[m, \[Tau]]τ] \[Beta]β Sin[\[Theta]]Sin[θ])/\[Sqrt]√(1 - \[Beta]^2β^2),  
   0, (Subscript[    mSubscript[m, \[Tau]]τ] \[Beta]β Cos[\[Theta]]Cos[θ])/\[Sqrt]√(1 - \[Beta]^2β^2)};

    p4 = {Subscript[   mSubscript[m, \[Tau]]τ]/\[Sqrt]√(1 - \[Beta]^2β^2), -((    Subscript[m, \[Tau]]τ] \[Beta]β Sin[\[Theta]]Sin[θ])/\[Sqrt]√(1 - \[Beta]^2β^2)),  
   0, -((Subscript[m, \[Tau]]τ] \[Beta]β Cos[\[Theta]]Cos[θ])/\[Sqrt]√(1 - \[Beta]^2β^2))};

    i3n = {0, 0, 1, 0};

    i3r = {0, -Cos[\[Theta]]Cos[θ], 0, Sin[\[Theta]]Sin[θ]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value.This is what i tried

    Sum[LeviCivitaTensor[4][[\[Mu]Sum[LeviCivitaTensor[4][[μ, \[Nu]ν, \[Alpha]α, \[Beta]]]β]] p3[[\[Alpha]]]p3[[α]] \p4[[\[Beta]]]p4[[β]] i3n[[\[Mu]]]i3n[[μ]] i3r[[\[Nu]]]i3r[[ν]], 
 {\[Mu]μ, 1, 4}, {\[Nu]ν, 1, 4}, {\[Alpha]α, 1, 4}, {\[Beta]β, 1, 4}]

But I get errors that $\frac{1}{0}$ is encountered. How do I fix it? I am at a loss please help.

I have the following vectors:

    p3 = {Subscript[m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), (   Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2),    0, (Subscript[    m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2)};

    p4 = {Subscript[   m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), -((    Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2)),    0, -((Subscript[m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2))};

    i3n = {0, 0, 1, 0};

    i3r = {0, -Cos[\[Theta]], 0, Sin[\[Theta]]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value.This is what i tried

    Sum[LeviCivitaTensor[4][[\[Mu], \[Nu], \[Alpha], \[Beta]]] p3[[\[Alpha]]] \p4[[\[Beta]]] i3n[[\[Mu]]] i3r[[\[Nu]]], {\[Mu], 1, 4}, {\[Nu], 1, 4}, {\[Alpha], 1, 4}, {\[Beta], 1, 4}]

But I get errors that $\frac{1}{0}$ is encountered. How do I fix it? I am at a loss please help.

I have the following vectors:

p3 = {Subscript[m, τ]/√(1 - β^2), (Subscript[m, τ] β Sin[θ])/√(1 - β^2),  
   0, (Subscript[m, τ] β Cos[θ])/√(1 - β^2)};

p4 = {Subscript[m, τ]/√(1 - β^2), -((Subscript[m, τ] β Sin[θ])/√(1 - β^2)),  
   0, -((Subscript[m, τ] β Cos[θ])/√(1 - β^2))};

i3n = {0, 0, 1, 0};

i3r = {0, -Cos[θ], 0, Sin[θ]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value.This is what i tried

Sum[LeviCivitaTensor[4][[μ, ν, α, β]] p3[[α]] p4[[β]] i3n[[μ]] i3r[[ν]], 
 {μ, 1, 4}, {ν, 1, 4}, {α, 1, 4}, {β, 1, 4}]

But I get errors that $\frac{1}{0}$ is encountered. How do I fix it? I am at a loss please help.

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edited Aug 21 at 12:48

user64494

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Contracting a Levi Civita Tensor-Civita tensor with vectors

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edited Aug 21 at 5:50

Lelouch

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I have the following vectors:

    p3 = {Subscript[m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), (   Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2),    0, (Subscript[    m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2)};

    p4 = {Subscript[   m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), -((    Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2)),    0, -((Subscript[m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2))};

    i3n = {0, 0, 1, 0};

    i3r = {0, -Cos[\[Theta]], 0, Sin[\[Theta]]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value.This is what i tried

    Sum[LeviCivitaTensor[4][[\[Mu], \[Nu], \[Alpha], \[Beta]]] p3[[\[Alpha]]] \p4[[\[Beta]]] i3n[[\[Mu]]] i3r[[\[Nu]]], {\[Mu], 1, 4}, {\[Nu], 1, 4}, {\[Alpha], 1, 4}, {\[Beta], 1, 4}]

But I get errors that $\frac{1}{0}$ is encountered. How do I dofix it? I am at a loss please help.

I have the following vectors:

    p3 = {Subscript[m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), (   Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2),    0, (Subscript[    m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2)};

    p4 = {Subscript[   m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), -((    Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2)),    0, -((Subscript[m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2))};

    i3n = {0, 0, 1, 0};

    i3r = {0, -Cos[\[Theta]], 0, Sin[\[Theta]]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value. How do I do it? I am at a loss please help.

I have the following vectors:

    p3 = {Subscript[m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), (   Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2),    0, (Subscript[    m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2)};

    p4 = {Subscript[   m, \[Tau]]/\[Sqrt](1 - \[Beta]^2), -((    Subscript[m, \[Tau]] \[Beta] Sin[\[Theta]])/\[Sqrt](1 - \[Beta]^2)),    0, -((Subscript[m, \[Tau]] \[Beta] Cos[\[Theta]])/\[Sqrt](1 - \[Beta]^2))};

    i3n = {0, 0, 1, 0};

    i3r = {0, -Cos[\[Theta]], 0, Sin[\[Theta]]};

I want to contract them with a Levi Civita tensor of order 4 to get a scalar value.This is what i tried

    Sum[LeviCivitaTensor[4][[\[Mu], \[Nu], \[Alpha], \[Beta]]] p3[[\[Alpha]]] \p4[[\[Beta]]] i3n[[\[Mu]]] i3r[[\[Nu]]], {\[Mu], 1, 4}, {\[Nu], 1, 4}, {\[Alpha], 1, 4}, {\[Beta], 1, 4}]

But I get errors that $\frac{1}{0}$ is encountered. How do I fix it? I am at a loss please help.

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asked Aug 21 at 5:34

Lelouch

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Contracting a Levi Civita Tensor-Civita tensor with vectors