Why are antiparticles associated with spin-flipped spinors?
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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
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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
Read more on Brainly
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