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In the book writing: ...consider the color invariant:

(t[itex]^{a}[/itex])[itex]_{ij}[/itex](t[itex]^{a}[/itex])[itex]_{kl}[/itex](18.38).The indices i,k transform according to to 3 representation of color; the indices j,l transform according to

3[itex]^{-}[/itex].Thus,(18.38) must be a linear combination of the two possible way to contract these indices,

Aδ[itex]_{il}[/itex]δ[itex]_{kj}[/itex]+Bδ[itex]_{ij}[/itex]δ[itex]_{kl}[/itex](18.39).

The constant A and B can be determined by contracting (18.38) and (18.39) with δ[itex]_{ij}[/itex] and with δ[itex]_{jk}[/itex].....

I do not understand why (18.38)must be a linear combination as (18.39)?

Thank you very much for your kind helping.

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# A question in QFT book of Peskin&Schoeder?

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