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 LeviCivita 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 antiselfdual 't Hooft symbols. More explicitly, these symbols are and They satisfy the selfduality and the antiselfduality properties: Some other properties are The same holds for except for
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