- #1
Hepth
Gold Member
- 464
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In particle physics, we commonly have the gamma matrices, whose conjugate transpose is the raised or lowered index. Does the same rule apply to ANY indexed quantity? What about to scalar/vectors like momentum.
Is the conjugate of momentum:
[tex]
\left(q_\mu\right)^\dagger = q^\mu
[/tex]
The reason I ask is I am trying to compute:
[tex]
\left(\sigma_{\mu\nu} q^\nu \right)^\dagger=
[/tex]
I get:
[tex]
\left(\sigma_{\mu\nu}\right)^\dagger =-\sigma^{\nu \mu}
[/tex]
but, since the q is a "scalar" quantity when summed over, it doesn't change any signs under the adjoint, correct?
Is the conjugate of momentum:
[tex]
\left(q_\mu\right)^\dagger = q^\mu
[/tex]
The reason I ask is I am trying to compute:
[tex]
\left(\sigma_{\mu\nu} q^\nu \right)^\dagger=
[/tex]
I get:
[tex]
\left(\sigma_{\mu\nu}\right)^\dagger =-\sigma^{\nu \mu}
[/tex]
but, since the q is a "scalar" quantity when summed over, it doesn't change any signs under the adjoint, correct?
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