Why are antiparticles associated with spin-flipped spinors?
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In section 2.2 of Elvang and Huang's Scattering Amplitudes in Gauge Theory and Gravity, beneath equation (2.9), it is mentioned that u±=v∓u±=v∓, where u±u± are massless spinors corresponding to helicity eigenstates for particles, and v∓v∓ are those for antiparticles.
Why is this true in general? Or is it a just a convention for associating certain antiparticle spinors with particle spinors? From equation (3.136) in section 3.6 of Peskin and Schroeder, we have
vs(p)=(p⋅σ−−−−√ξ−s−p⋅σ¯−−−−√ξ−s),vs(p)=(p⋅σξ−s−p⋅σ¯ξ−s),
which seems to suggest that it is just a matter of choosingsome basis of two-component spinors ξ−sξ−s, which in this case happen to have opposite spin from those used in us(p)us(p). With this choice of vs(p)vs(p), it is straightforward to get u±=v∓u±=v∓ in the massless limit.
I am sure that there is some physical justification for this but what is it? Elvang and Huang suggests using crossing symmetry but the choice of relating s and t channel diagrams seems as arbitrary as any convention.
Why is this true in general? Or is it a just a convention for associating certain antiparticle spinors with particle spinors? From equation (3.136) in section 3.6 of Peskin and Schroeder, we have
vs(p)=(p⋅σ−−−−√ξ−s−p⋅σ¯−−−−√ξ−s),vs(p)=(p⋅σξ−s−p⋅σ¯ξ−s),
which seems to suggest that it is just a matter of choosingsome basis of two-component spinors ξ−sξ−s, which in this case happen to have opposite spin from those used in us(p)us(p). With this choice of vs(p)vs(p), it is straightforward to get u±=v∓u±=v∓ in the massless limit.
I am sure that there is some physical justification for this but what is it? Elvang and Huang suggests using crossing symmetry but the choice of relating s and t channel diagrams seems as arbitrary as any convention.
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If a particle and an antiparticle are created, the total spin must be zero, for the low of conservation of angular momentum.
Hence if the electron is measured to be spin up, the positron will have necessarily spin down, and the particles are entangled.
And indeed this is the case only if the particles are entangled (which is always the case for particle-antiparticle pairs)
Hence if the electron is measured to be spin up, the positron will have necessarily spin down, and the particles are entangled.
And indeed this is the case only if the particles are entangled (which is always the case for particle-antiparticle pairs)
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