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The bar notation is necessary in order to make all of the quantities above Lorentz invariant. In short the relationship between the bar'ed quantitites and charge conjugates of fermions have to do with taking the hermitian conjugate of the creation / annihilation opeartors. Let us focus for now on a free theory of Fermions. A Dirac Fermion can be written down ...

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This is to supplement Andrew's answer and focuses on other sub-questions. Electricity, more precisely electric current, is the flow of electric charges. Electrons are very convenient charge carriers as they move relatively easily (though not without collisions) through a lattice-like grid of nuclei in a metal (have a look at the sea of electrons model for ...

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I think you are really asking two questions. Can positrons serve as charge carriers in electric circuits? Theoretically, yes, if you replaced every matter particle in an electric circuit with a corresponding anti-matter particle, the circuit would work the same way (except the flow of electric charge would be in the opposite direction). However in practice ...

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Only a small fraction of the so-called cosmic rays, which are actually high energy particles from different astrophysical sources that reach the Earth are antimatter, and you are right: If they are antimatter, they annihilate as soon as they hit some corresponding matter particle (for example when a positron hits an electron) in the atmosphere. Nevertheless, ...

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The photon is its own antiparticle, so "anti-light" is just light.

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It is not known if neutrinos are Majorana fermions, but regardless even if they are not, it a pair of photons can in principle turn into a neutrino-antineutrino like in this diagram (on the left are the incoming photons, on the right are the resulting neutrino and antineutrino): However, there is no tree-level process that would do the same thing (neutrinos ...

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Do you mean this type of diagram?: with neutrino antineutrino outgoing? It is not possible to first order, because the photon does not couple with the weak interaction and neutrinos only couple weakly. This means a loop ,as in photon photon interactiion would be necessary (The left one is the virtual photon interacting with the field and allowing momentum ...

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Photons are the quanta of the electromagnetic interaction that couple via the electric charge to other fields. As neutrinos don't have any electric charge, photons cannot couple to them. So neutrinos cannot be generated in leading order out of photons (there might be a more complex process of higher order with intermediate states involving the weak ...

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In QFT, when making a field operator, negative frequency solutions correspond to annihilation operators while positive frequency solutions correspond to creation operators. Not worrying about normalizations and things like that, $$\hat \phi(x) \propto \int d^3 k \left( \hat a(k) e^{- i k \cdot x} + \hat a^\dagger(k) e^{ i k \cdot x} \right).$$ Furthermore, ...

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Identifying the positron and electron component cannot be done as straightforwardly. In fact, there is no way to do this by a local operation on the field, the positron and electron component are hidden in the field global mode by global mode, as already stated by Andrew. However, it is true that for a complex field $\phi$, it is often instructive to ...

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No. For example if you take a free electron moving with momentum $\vec{k}$, then its wavefunction is complex $\psi \sim e^{i \vec{k}\cdot \vec{x}}$. If for some reason you had a prejudice that caused you to prefer working with real and imaginary parts instead of complex numbers, you could write $\psi=\psi_R+i\psi_I$, with $\psi_R\sim \cos(\vec{k}\cdot\vec{x})... 3 Only the neutral charm mesons (${ { D }^{ 0 } }$and$\overline { { D }^{ 0 } }\$) can change from particle to antiparticle, and the neutral charm mesons have no charge.

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