# Particles and antiparticles in compex field

1. ### spookyfish

53
Hi. I am confused about something related to the creation of particles/antiparticles in a complex scalar field.
I read in the literature that $\phi(x)|0\rangle$ describes the creation of a particle at point $x$. But given that

$$\phi(x) = \int \frac{d^3 p}{\sqrt{(2\pi)^3 2E_p}} \left(a(p)e^{-ipx}+b^\dagger (p)e^{ipx}\right)$$

then in $\phi(x)|0\rangle$ only the $b^\dagger(p)$ term contributes, i.e.

$$\phi(x)|0\rangle= \int \frac{d^3 p}{\sqrt{(2\pi)^3 2E_p}}e^{ipx} b^\dagger(p)|0\rangle$$

from which it seems that an anti-particle (created by $b^\dagger(p)$) is created at $x$.

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3. ### fzero

2,601
We don't have the original text that you read around to nitpick, but if ##\phi(x)## creates the antiparticle, then ##\phi^\dagger(x)## creates the particle. The original reference could have been

1. sloppy
2. using a different definition of particle vs antiparticle
3. referring to a real scalar field

etc. We simply can't be sure without knowing precisely what you read and the context in which the author stated that.

4. ### spookyfish

53
Thanks. In fact, my problem was with something I read in the internet related to the literature, and I think it was simply wrong, so the definitions I wrote above work.