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For this question, note that curly brackets {..} is an anti-commutator eg. {AB} = AB+BA where A and B are matrices.
Also note that I4 is the identity 4x4 matrix.
I would like to understand why { γµ,{γργσ} } = 2 { γµ, I4 }[tex]\eta^{\rho \sigma} [/tex]
I understand that { γµ,{γργσ} } = 2{ γµ,[tex]\eta^{\rho \sigma}I_4[/tex] } (as {γρ,γσ}= [tex]2\eta^{\rho \sigma}[/tex]) but why can we take [tex]\eta^{\rho \sigma}[/tex] out of the anti commutator, like in the expression above?
If we can, this means [tex]\gamma^\mu \eta^{\rho \sigma} = \eta^{\rho \sigma}\gamma^\mu [/tex]. Why is this necessarily true?
Also note that I4 is the identity 4x4 matrix.
I would like to understand why { γµ,{γργσ} } = 2 { γµ, I4 }[tex]\eta^{\rho \sigma} [/tex]
I understand that { γµ,{γργσ} } = 2{ γµ,[tex]\eta^{\rho \sigma}I_4[/tex] } (as {γρ,γσ}= [tex]2\eta^{\rho \sigma}[/tex]) but why can we take [tex]\eta^{\rho \sigma}[/tex] out of the anti commutator, like in the expression above?
If we can, this means [tex]\gamma^\mu \eta^{\rho \sigma} = \eta^{\rho \sigma}\gamma^\mu [/tex]. Why is this necessarily true?