Student Friendly Introduction to QFT · Problem 8

Looking Backward and Looking Forward: Book Summary and What's Next

Physics — QFT · compton-scattering-kinematics

Problem

Show that, for Compton scattering,

p^\mu k_\mu = p^{\prime\mu} k^\prime_\mu

. Hint: Square the conservation relation (17-139). That is, find

\left(p^\mu + k^\mu\right)\left(p_\mu + k_\mu\right) = \left(p^{\prime\mu} + k^{\prime\mu}\right)\left(p^\prime_\mu + k^\prime_\mu\right)

. Also, show that

p^{\prime\mu} k_\mu = p^\mu k_\mu

. Hint: Start by re-arranging the conservation relation.