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A charged particle say an electron carries a negative charge and it will experience a force when there is an electric field, like charges repel and unlike charges attract so does this means an electric field either carry charge(s) or behave like charge, or charge can only be applied to particle? Also can electric field be neutral?

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Yes, indeed fields can carry charge, however the EM field (also called the photon field) does not carry any charge. If it did, then EM fields could affect the trajectories of photons.

I will do my best to explain why below, but there's no way to do it without group theory (as far as I know).

The meaning of carrying a charge means that it transforms under some non-trivial representation of the gauge group. So, for instance in EM the fermions $\Psi$ transform non-trivially under the gauge group $U(1)_{EM}$, however the EM field $A_\mu(x)$ transforms under the trivial representation of $U(1)_{EM}$ (meaning it doesn't transform at all), however this is in particular a special case, since $U(1)$ is an abelian group.

However, fields can carry a charge. In the strong force the fermions $\Psi$ carry a different kind of charge: They carry an $SU(3)_c$ color charge, and they transform under the fundamental representation of $SU(3)_c$ (i.e. they have 3 color indices). Moreover, since $SU(3)_c$ is a non-abelian group it turns out that in order for this to be a symmetry of our lagrangian, the gauge fields $A_\mu^a$ do transform under the gauge group, meaning that they indeed do carry a color charge as well. However, they are in what is called the adjoint representation of $SU(3)$, and so carry 8-color indices (which is what the $a$ in $A_\mu^a$ represents) .

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  • $\begingroup$ Hi thanks for the answer, what prerequisites do I need in order to understand this? Especially the parts when you explain why em field do not carry charge because it do not transform. $\endgroup$ – user6760 Dec 24 '18 at 2:07
  • $\begingroup$ Right. I didn't know what level you were on, so I just thought I'd give an answer at the level I knew it which is Quantum Field Theory (QFT). Before getting to QFT, the fact that the photon (the mediator of the EM interaction) does not have a charge is simply an experimental fact. $\endgroup$ – InertialObserver Dec 24 '18 at 2:10
  • $\begingroup$ I'm learning quantum mechanics and other advance physics by asking random strangers and looking up social media, i took GCSE O level physics before. $\endgroup$ – user6760 Dec 24 '18 at 2:20
  • $\begingroup$ The question asks about the electric field carrying a charge, not fields in general. And presumably they're asking about electric charge, not color charge. $\endgroup$ – The Photon Dec 24 '18 at 7:10
  • $\begingroup$ @user6760 Maybe this is another way to express InertialObserver's answer: The electric field does not have electric charge because if it did, it would attract/repel itself (and photons). An example of this is the strong force, in which the field that mediates the force is color-charged just like the quarks are color-charged. As a result, the strong force field has a tendency to "attract itself" into a rope-like configuration between the quarks, which is related to why quarks are confined. The electric field, in contrast, does not have such a tendency, so electric charges aren't confined. $\endgroup$ – Chiral Anomaly Dec 24 '18 at 16:13

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