| 11. | This antisymmetry is required by the Pauli principle and the fact that electrons are fermions.
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| 12. | Conversely, the same statement holds for antisymmetry with respect to a conserved symmetry element.
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| 13. | And antisymmetry under exchange means that.
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| 14. | Antisymmetry follows from antisymmetry of the Lie bracket on and antisymmetry of the 2-cocycle.
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| 15. | Antisymmetry follows from antisymmetry of the Lie bracket on and antisymmetry of the 2-cocycle.
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| 16. | Antisymmetry follows from antisymmetry of the Lie bracket on and antisymmetry of the 2-cocycle.
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| 17. | Otherwise the sum would again be zero due to the antisymmetry, thus representing a physically impossible state.
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| 18. | The key definitive property of the symbol is " total antisymmetry " in all the indices.
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| 19. | However, in this way one does not take advantage of the partial antisymmetry that is already present.
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| 20. | This antisymmetry holds even when the characteristic is 2, although with characteristic 2 antisymmetry is equivalent to symmetry.
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