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Particles and antiparticles in compex field

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Nov3-13, 12:05 PM
P: 48
Hi. I am confused about something related to the creation of particles/antiparticles in a complex scalar field.
I read in the literature that [itex] \phi(x)|0\rangle [/itex] describes the creation of a particle at point [itex] x [/itex]. But given that

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

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

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

from which it seems that an anti-particle (created by [itex] b^\dagger(p) [/itex]) is created at [itex] x [/itex].
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Nov3-13, 12:26 PM
Sci Advisor
HW Helper
PF Gold
P: 2,603
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.
Nov4-13, 05:52 PM
P: 48
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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