Particles and antiparticles in compex field

  1. 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].
  2. jcsd
  3. fzero

    fzero 3,005
    Science Advisor
    Homework Helper
    Gold Member

    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. 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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