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Qmechanic
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Levi civita-Civita and Kronecker Delta

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Davide Morgante
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To prove this, \begin{gather} \sum_{pq} \epsilon_{ipq} \epsilon_{jpq} = 2*\delta_{ij} \end{gather}$$ \sum_{pq} \epsilon_{ipq} \epsilon_{jpq} = 2\delta_{ij} $$

I used levi civitaLevi-Civita and delta relation,

\begin{gather} \sum_{q} \epsilon_{ipq}*\epsilon_{jpq} = \delta_{ij}*\delta_{pp}-\delta_{ip}*\delta_{pj} \\ \ then\ first\ and\ second \ term \ both\ will\ be\ \ just \ \delta_{ij} so\ both\ cancel\ out\ \end{gather}$$ \sum_{q} \epsilon_{ipq}\epsilon_{jpq} = \delta_{ij}\delta_{pp}-\delta_{ip}\delta_{pj} $$ then first and second term both will be just $\delta_{ij}$ so both cancel out.

whereWhere it is going wrong  ? since Since using that relation I am getting zero not as twice of delta.

To prove this, \begin{gather} \sum_{pq} \epsilon_{ipq} \epsilon_{jpq} = 2*\delta_{ij} \end{gather}

I used levi civita and delta relation,

\begin{gather} \sum_{q} \epsilon_{ipq}*\epsilon_{jpq} = \delta_{ij}*\delta_{pp}-\delta_{ip}*\delta_{pj} \\ \ then\ first\ and\ second \ term \ both\ will\ be\ \ just \ \delta_{ij} so\ both\ cancel\ out\ \end{gather}

where it is going wrong  ? since using that relation I am getting zero not as twice of delta

To prove this, $$ \sum_{pq} \epsilon_{ipq} \epsilon_{jpq} = 2\delta_{ij} $$

I used Levi-Civita and delta relation

$$ \sum_{q} \epsilon_{ipq}\epsilon_{jpq} = \delta_{ij}\delta_{pp}-\delta_{ip}\delta_{pj} $$ then first and second term both will be just $\delta_{ij}$ so both cancel out.

Where it is going wrong? Since using that relation I am getting zero not as twice of delta.

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Levi civita and Kronecker Delta

To prove this, \begin{gather} \sum_{pq} \epsilon_{ipq} \epsilon_{jpq} = 2*\delta_{ij} \end{gather}

I used levi civita and delta relation,

\begin{gather} \sum_{q} \epsilon_{ipq}*\epsilon_{jpq} = \delta_{ij}*\delta_{pp}-\delta_{ip}*\delta_{pj} \\ \ then\ first\ and\ second \ term \ both\ will\ be\ \ just \ \delta_{ij} so\ both\ cancel\ out\ \end{gather}

where it is going wrong ? since using that relation I am getting zero not as twice of delta