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I've been asked to prove the following identity

[tex]tr(\gamma^{\mu} \gamma^{\nu} \gamma^{\rho} \gamma^{\sigma}) = 4 (\eta ^{\mu \nu} \eta ^{\rho \sigma} - \eta ^{\mu \rho} \eta ^{\nu \sigma} + \eta ^{\mu \sigma} \eta ^{\nu \rho})[/tex]

I know that

[tex]tr(\gamma^{\mu} \gamma^{\nu}) = 4 \eta^{\mu \nu}[/tex]

which means I would expect something of the form

[tex]tr(\gamma^{\mu} \gamma^{\nu} \gamma^{\rho} \gamma^{\sigma}) = 4 \eta^{\mu \nu} \eta^{\rho \sigma}[/tex]

Any suggestions?

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# Gamma matrices

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