- #1
Kalimaa23
- 279
- 0
Greetings,
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?
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?