# A question on particle-antiparticle chirality.

Concerning chirality, I recently read that matter is left-handed and that antimatter is right-handed. Are matter particles left- handed as seen from in front or behind? As an electron can have spin up or spin down and a positron has opposite spin up and opposite spin down. So I was thinking that to determine the difference between them we mast have a preference of from in front or behind.

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Meir Achuz
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For particles, 'left handed' means that the spin is in the opposite direction of the momentum.
That could be interpreted as meaning you are looking at the rotation of the spin (if it did rotate) from behind.
This can lead to some confusion for a photon. A left handed photon corresponds to right handed circular polarization, because the polarization of light is as it comes toward you.

Concerning chirality, I recently read that matter is left-handed and that antimatter is right-handed.
This is not the case. Both matter and anti-matter particles are made up of both left and right chirality components (essentially they are a superposition of them). Except for neutrinos, which are only left chiral (with the corresponding anti-neutrinos being right chiral)

Are matter particles left- handed as seen from in front or behind? As an electron can have spin up or spin down and a positron has opposite spin up and opposite spin down. So I was thinking that to determine the difference between them we mast have a preference of from in front or behind.
One thing to keep in mind is that "chirality" and "helicity" are different (but related) operators, but the words "left-handed" and "right-handed" are used to describe the eigenstates of both of them. Only for massless particles do the eigenstates of each coincide.

What you are describing is helicity, which is the projection of spin in the direction of motion of a particle, i.e. $$h = \vec{S}\cdot\vec{p}$$ A particle is "right handed" if this comes out positive , i.e. the spin and momentum vectors point in the same direction. This is not Lorentz invariant though, because if your particle is massive then you can boost to a reference frame where the momentum vector is reversed, so the helicity is also reversed.

Chirality is more abstract, but is important in the Standard Model for determining if a particle interacts with the weak force or not. It is not an awesome article, but you could check out this wikipedia page for a little more detail: http://en.wikipedia.org/wiki/Chirality_(physics [Broken])

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