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The 't Hooft η symbol is a symbol which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend between the Kronecker delta and the Levi-Civita symbol. It was introduced by Gerard 't Hooft. It is used in the construction of the BPST instanton. ηaμν is the 't Hooft symbol: In other words, they are defined by () where the latter are the anti-self-dual 't Hooft symbols. More explicitly, these symbols are and They satisfy the self-duality and the anti-self-duality properties: Some other properties are The same holds for except for

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  • 't Hooft symbol
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  • The 't Hooft η symbol is a symbol which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend between the Kronecker delta and the Levi-Civita symbol. It was introduced by Gerard 't Hooft. It is used in the construction of the BPST instanton. ηaμν is the 't Hooft symbol: In other words, they are defined by () where the latter are the anti-self-dual 't Hooft symbols. More explicitly, these symbols are and They satisfy the self-duality and the anti-self-duality properties: Some other properties are The same holds for except for
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  • The 't Hooft η symbol is a symbol which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend between the Kronecker delta and the Levi-Civita symbol. It was introduced by Gerard 't Hooft. It is used in the construction of the BPST instanton. ηaμν is the 't Hooft symbol: In other words, they are defined by () where the latter are the anti-self-dual 't Hooft symbols. More explicitly, these symbols are and They satisfy the self-duality and the anti-self-duality properties: Some other properties are The same holds for except for and Obviously due to differentduality properties. Many properties of these are tabulated in the appendix of 't Hooft's paper and also in the article by Belitsky et al.
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