I am self-studying QFT and I came to the point of quantizing the Dirac field. The Dirac field expanded in terms of creation/annihilation operators is:


Then, the notes I am studying suggest that:


It looks like the creation/annihilation operator commutes with the spinors so that for example $$(b_{\vec{p}}^{s}u^{s}(\vec{p}))^{\dagger}=u^{s\dagger}(\vec{p})b_{\vec{p}}^{s\dagger}=b_{\vec{p}}^{s\dagger}u^{s\dagger}(\vec{p}).$$

Does this happen because the creation and annihilation operators act on states $|p\rangle$, and not on spinors?


1 Answer 1


The spinors $u^s(p), v^s(p)$ are not operators, they are just (an array of) numbers and therefore commute with the creation/annihilation operators.


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