Particles and antiparticles in compex field

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SUMMARY

The discussion clarifies the creation of particles and antiparticles in a complex scalar field, specifically addressing the operator notation \(\phi(x)|0\rangle\). It establishes that the term \(b^\dagger(p)\) in the expression \(\phi(x) = \int \frac{d^3 p}{\sqrt{(2\pi)^3 2E_p}} \left(a(p)e^{-ipx}+b^\dagger (p)e^{ipx}\right)\) indicates that an antiparticle is created at point \(x\). The discussion emphasizes that \(\phi^\dagger(x)\) is responsible for creating particles, highlighting potential confusion in literature regarding definitions of particles and antiparticles.

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spookyfish
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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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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.
 
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.
 

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