DuckAmuck
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- Can the gamma matrices really represent any anti-symmetric tensor?
The sigma tensor composed of the commutator of gamma matrices is said to be able to represent any anti-symmetric tensor.
\sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu]
However, it is not clear how one can arrive at something like the electromagnetic tensor.
F_{\mu\nu} = a \bar{\psi} \sigma_{\mu\nu} \psi ?
Any clarity will be appreciated.
\sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu]
However, it is not clear how one can arrive at something like the electromagnetic tensor.
F_{\mu\nu} = a \bar{\psi} \sigma_{\mu\nu} \psi ?
Any clarity will be appreciated.