17.5. Reflection amplitude Consider the following scattering amplitudes of a particle A and its anti-particle A

| A(θ1)A(θ2) = S(θ) | A(θ2)A(θ1),

| A(θ1)A(θ2) = t(θ) | A(θ2)A(θ1)+r(θ) | A(θ2)A(θ1).

a. Prove that it holds S(θ)S(−θ) = t(θ) t(−θ)+r(θ) r(−θ) = 1 t(θ) r(−θ)+r(θ) t(−θ) = 0 t(θ) = S(iπ −θ), r(θ) = r(iπ −θ).

b. Prove that if the particles A and A are uniquely distinguishable by their different eigenvalues of the conserved charges, then the reflection amplitude vanishes, i.e.
r(θ) = 0.