An electron field is a superposition of(adsbygoogle = window.adsbygoogle || []).push({}); twofour-component Dirac spinors, one of them multiplied with a creation operator and an exponential with negative energy, the other multiplied with an annihilation operator and an exponential with positive energy.

So I assume one Dirac spinor creates a particle (electron), the other annihaltes an antiparticle (positron). The conjugated electron field does vice versa.

But then each of these two spinors consists of two Weyl spinors, i.e. each Dirac spinor represents two electrons (up and down or left-chiral and right-chiral) and two positrons (up and down or left-chiral and right-chiral).

So why do we need then two Dirac spinors (a superposition of them) to account for electrons and positrons? How and why do these 8 (2x4) components describe electrons and positrons? Does the Dirac equation restrict and reduce the number of compents somewhat? How?

thank you

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# Dirac spinor and antiparticles

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