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Chiral states: |
Lc |
Rc |
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Based on spinor structure |
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Helicity states |
LHH |
RHH |
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Helicity is spin along z-axis
where the z-axis is chosen along the momentum direction: |
- |
+ |
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[The difference between a helicity and spin formalisms appears when there is more than one particle. Each particle will then define a new z-axis for spin projection]
There are two states that span the spin space for a particle and two states that span the space for an antiparticle. One can either use the helicity or the chiral basis.
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In the limit of mè0
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particle |
Left Handed |
Right Handed |
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Right Handed |
Left Handed |
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antiparticle |
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- Helicity operator commutes with free particle Hamiltonian
- Helicity conserved but not a Lorentz invariant
- Chirality not same as helicity for massive particles
- Chirality not conserved but a Lorentz invariant
- Freely propagating left-chiral projection will develop a right-chiral component
- Note PR projects out
right-handed particles and left-handed anti-particles.
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Momentum Possible Spin (conserve ang. Mom) |
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Possible spin for weak interation
due to Lc for massless
neutrino |
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Neutrino |
Muon |
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Hel - LHH |
Hel - LHH |
Angular momentum |
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Chiral Lc |
Chiral Lc |
Weak interaction |
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Neutrino M=0 |
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mass= 0
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Anti muon (electron) |
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Angular momentum conservation
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