Griffiths Introduction to Elementary Particles · Problem 7.26

Electrodynamics of Quarks and Hadrons — David J. Griffiths

Physics — QFT · casimir-trick-antiparticles

Problem

Work out the analog to Casimir's trick (7.123) for antiparticles ∑all spins[vˉ(a)Γ1v(b)][vˉ(a)Γ2v(b)]∗\sum_{\text{all spins}} [\bar{v}(a)\Gamma_1 v(b)][\bar{v}(a)\Gamma_2 v(b)]^* and for the ``mixed'' cases ∑all spins[uˉ(a)Γ1v(b)][uˉ(a)Γ2v(b)]∗,∑all spins[vˉ(a)Γ1u(b)][vˉ(a)Γ2u(b)]∗\sum_{\text{all spins}} [\bar{u}(a)\Gamma_1 v(b)][\bar{u}(a)\Gamma_2 v(b)]^*, \qquad \sum_{\text{all spins}} [\bar{v}(a)\Gamma_1 u(b)][\bar{v}(a)\Gamma_2 u(b)]^*

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