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There is, in the Alekseev paper a rather strange description of the dark matter. In introduction he writes: 'It was postulated that the source of antigravitation is “dark matter” which inferred to exist from gravitational effects on visible matter'. The search for the dark matter was triggered by the observations showing the conventional gravitational ...

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The point is that a Dirac field isn't really a solution for an electronand positron but instead an electron and the conjugate of the positron. This means that the Dirac electron field does indeed obey, $$e ^{ i \alpha (x) Q } \psi = e ^{ - i \alpha (x) } \psi$$ Such misconceptions are dissolved if one works in the Weyl ...

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The second one is a "quark diagram" or "quark model diagram". These are not 'true' Feynman diagrams, as they only represent the quark fields. The gluon field is implied, and it's an exercise for the reader to fill in the gaps. The only pedagogical source I can find is this: http://ned.ipac.caltech.edu/level5/Cottingham/Cott1_5.html (See the caption of ...

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In your second diagram, there is implicitly a gauge boson source of your $q\bar{q}$ pair production. It could be a gluon, a photon or a $Z^0$. This gauge boson has to be attached to something, reasonably your single quark leg as in the first diagram.

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Well, quark anti-quark pair can be created by a photon in a process like $$\mu^- + \mu^+ \to \gamma \to q + \bar{q} \,,$$ which is just the time reversal of a typical Drell-Yan process, with the intermediate photon shown explicitly. Not sure if this really answers your question since you seem to be assuming a single quark initial state.

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It is my understanding that antiparticles are the opposites of each other such as electron positron pair -- which means the positron is an electron flipped 180 degrees on its axis --same angular velocity, same size but PHOTONS are not particles, they are electromagnetic waves which rotate 360 deg for every wavelength so in effect are "positive" 50% of time ...

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