Student Friendly Introduction to QFT · Problem 8.5

The Vacuum Revisited

Physics — QFT · normal-ordering-anti-commutators

Problem

a) Show

N\left\{\left[\bar{\psi}^+(x_1), \psi^-(x_2)\right]_+\right\} = 0

, even though the anti-commutator shown does not equal zero. b) Using a), show that

N\left\{\phi(x_1)\phi^\dagger(x_2)\psi(x_3)\bar{\psi}(x_4)\ldots\right\} = N\left\{-\phi(x_1)\phi^\dagger(x_2)\bar{\psi}(x_4)\psi(x_3)\ldots\right\}