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I'd like to understand crossing symmetry in QFT better. I've only found somewhat detailed treatments of the scalar case, somewhat contradictory comments for the spin-1/2 case, and nothing so far for the spin-1 case.

Broadly speaking, does anyone have some good references for a rigorous treatment of the crossing symmetry of particles with non-zero spin?

Speaking of the spin-1/2 case, Peskin writes somewhat cryptically below Eq. 5.68 that when crossing spin-1/2 particles one gets an extra minus, but that "[t]he minus sign can be compensated by changing our phase convention for $v(k)$."

Weinberg, on the other hand, suggests that the minus sign comes from Fermi statistics and continues that "crossing symmetry is not an ordinary symmetry (it involves an analytic continuation in kinematic variables) and it is difficult to use it with any precision for general processes." (!)

So, in particular, what would the explicit spinors $u(p)$ and $v(p)$ be for Peskin under the different sign convention?

Further, is crossing symmetry trivial for spin-1 particles like it is for scalars?

Thank you very much for your help!

I'd like to understand crossing symmetry in QFT better. I've only found somewhat detailed treatments of the scalar case, somewhat contradictory comments for the spin-1/2 case, and nothing so far for the spin-1 case.

Broadly speaking, does anyone have some good references for a rigorous treatment of the crossing symmetry of particles with non-zero spin?

Speaking of the spin-1/2 case, Peskin writes somewhat cryptically below Eq. 5.68 that when crossing spin-1/2 particles one gets an extra minus, but that "[t]he minus sign can be compensated by changing our phase convention for $v(k)$."

Weinberg, on the other hand, suggests that the minus sign comes from Fermi statistics and continues that "crossing symmetry is not an ordinary symmetry (it involves an analytic continuation in kinematic variables) and it is difficult to use it with any precision for general processes." (!)

So, in particular, what would the explicit spinors $u(p)$ and $v(p)$ be for Peskin under the different sign convention?

Further, is crossing symmetry trivial for spin-1 particles like it is for scalars?

Thank you very much for your help!

I'd like to understand crossing symmetry in QFT better. I've only found somewhat detailed treatments of the scalar case, somewhat contradictory comments for the spin-1/2 case, and nothing so far for the spin-1 case.

Broadly speaking, does anyone have some good references for a rigorous treatment of the crossing symmetry of particles with non-zero spin?

Speaking of the spin-1/2 case, Peskin writes somewhat cryptically below Eq. 5.68 that when crossing spin-1/2 particles one gets an extra minus, but that "[t]he minus sign can be compensated by changing our phase convention for $v(k)$."

Weinberg, on the other hand, suggests that the minus sign comes from Fermi statistics and continues that "crossing symmetry is not an ordinary symmetry (it involves an analytic continuation in kinematic variables) and it is difficult to use it with any precision for general processes." (!)

So, in particular, what would the explicit spinors $u(p)$ and $v(p)$ be for Peskin under the different sign convention?

Further, is crossing symmetry trivial for spin-1 particles like it is for scalars?

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Crossing Symmetry for Particles with Spin

I'd like to understand crossing symmetry in QFT better. I've only found somewhat detailed treatments of the scalar case, somewhat contradictory comments for the spin-1/2 case, and nothing so far for the spin-1 case.

Broadly speaking, does anyone have some good references for a rigorous treatment of the crossing symmetry of particles with non-zero spin?

Speaking of the spin-1/2 case, Peskin writes somewhat cryptically below Eq. 5.68 that when crossing spin-1/2 particles one gets an extra minus, but that "[t]he minus sign can be compensated by changing our phase convention for $v(k)$."

Weinberg, on the other hand, suggests that the minus sign comes from Fermi statistics and continues that "crossing symmetry is not an ordinary symmetry (it involves an analytic continuation in kinematic variables) and it is difficult to use it with any precision for general processes." (!)

So, in particular, what would the explicit spinors $u(p)$ and $v(p)$ be for Peskin under the different sign convention?

Further, is crossing symmetry trivial for spin-1 particles like it is for scalars?

Thank you very much for your help!