- #1

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- 39

- Homework Statement
- Show that

epsilon_{ijkl} ( M^{ij} N^{kl} + N^{ij} M^{kl}) = 0

- Relevant Equations
- epsilon is the 4D anti-symmetric Levi-Cevita tensor. M and N are also anti-symmetric tensors.

ep_{ijkl} M^{ij} N^{kl} + ep_{ijkl}N^{ij} M^{kl}

The second term can be rewritten with indices swapped

ep_{klij} N^{kl}M^{ij}

Shuffle indices around in epsilon

ep{klij} = ep{ijkl}

Therefore the expression becomes

2ep_{ijkl}M^{ij}N^{kl}

Not zero.

What is wrong here?

The second term can be rewritten with indices swapped

ep_{klij} N^{kl}M^{ij}

Shuffle indices around in epsilon

ep{klij} = ep{ijkl}

Therefore the expression becomes

2ep_{ijkl}M^{ij}N^{kl}

Not zero.

What is wrong here?