| 11. | The importance of symmetric and antisymmetric states is ultimately based on empirical evidence.
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| 12. | The corresponding eigenvectors are the symmetric and antisymmetric states:
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| 13. | Similarly one can express elementary symmetric polynomials via traces over antisymmetric tensor powers.
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| 14. | Particles which exhibit antisymmetric states are called fermions.
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| 15. | Here juxtaposition is symmetric respectively antisymmetric multiplication in the symmetric and antisymmetric tensor algebra.
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| 16. | Here juxtaposition is symmetric respectively antisymmetric multiplication in the symmetric and antisymmetric tensor algebra.
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| 17. | Where is an arbitrary antisymmetric tensor in indices.
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| 18. | They are antisymmetric with respect to the other.
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| 19. | In other words, iteration is antisymmetric, and thus, a partial order.
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| 20. | :The tensors that show up in physics are usually either symmetric or antisymmetric.
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