# How to normalize wave functions in QFT? such as \lambda \phi 4 theory?

by mings6
Tags: functions, lambda, normalize, theory, wave
 Sci Advisor Thanks P: 2,329 In QFT the normalization of the field operators are defined via the equal-time commutation relations, $[\phi(t,\vec{x}),\Pi(t,\vec{y})]=\mathrm{i} \delta^{(3)}(\vec{x}-\vec{y}).$ Here $\Pi$ is the canonical field momentum for $\phi$. In $\phi^4$ theory, it's $\Pi(x)=\frac{\partial \mathcal{L}}{\partial \dot{\phi}(x)}=\dot{\phi}(x).$ For the asymptotically free states, symbolized by external legs in Feynman diagrams, the states are to be normalized in the usual way to $\delta$ distributions (supposed you have taken account of wave-function renormalization in the external legs, i.e., left out all self-energy insertions in them, see Weinberg, QT of Fields, vol. 1).