LiXinghe
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In 'Supersymmetry in Particle Physics, An Elementary Introduction', the author Ian Aitchison used for several times the following identity:
λa(ζ · ρ) + ζa(ρ · λ) + ρa(λ · ζ) = 0.
I know that this identity is called Schouten's Identity, which is correct when all the variables are common numbers. But, since the λ ζ and ρ are Grassmannian variables, we no longer have λ· λ=0. So how can we use this identity here, since the spinors here are anti-commuting?
λa(ζ · ρ) + ζa(ρ · λ) + ρa(λ · ζ) = 0.
I know that this identity is called Schouten's Identity, which is correct when all the variables are common numbers. But, since the λ ζ and ρ are Grassmannian variables, we no longer have λ· λ=0. So how can we use this identity here, since the spinors here are anti-commuting?