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Spinnor
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In the ψ below, there are 4 components for the Dirac spinnor times three possible color states for a total of 12 components for ψ?
Are there low energy, weak field limits of the above that allow us to consider classical color counterparts of electric current densities and electric charge densities?
Thanks for any help!
Thanks to ChrisVer for the original post!
ChrisVer said:...
Nevermind, to get the color current, you need the interactive Lagrangian:
[itex]L_{int}= -g_{3} \bar{ψ} γ^{μ}λ^{a} ψ A_{μ}^{a}/2 [/itex]
the corresponding conserved current (if you remember from the Dirac's current case) is:
[itex] J_{SU(3)}^{μa}= g_{3} \bar{ψ} γ^{μ}(λ^{a}/2) ψ[/itex]
What can we see from that? That we have 8 conserved currents. Each of them is individually conserved. The continuity relation for the currents, is given by their conservation, thus you have again 8 different continuity relations:
[itex]∂_{μ}J_{SU(3)}^{μa}= 0 [/itex]
and the color charge is:
[itex] Q_{c}=\int{d^{3}x J_{SU(3)}^{0a}}[/itex]
If they also carry electric charge, you'll get also another current, corresponding to [itex] U(1)_{Q} [/itex] interaction...
[/itex]
...
Are there low energy, weak field limits of the above that allow us to consider classical color counterparts of electric current densities and electric charge densities?
Thanks for any help!
Thanks to ChrisVer for the original post!