Particles and antiparticles in compex field

  1. Nov 3, 2013 #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. Nov 3, 2013 #2


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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.
  4. Nov 4, 2013 #3
    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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