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Particles and antiparticles in compex field 
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#1
Nov313, 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 antiparticle (created by [itex] b^\dagger(p) [/itex]) is created at [itex] x [/itex]. 


#2
Nov313, 12:26 PM

Sci Advisor
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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. 


#3
Nov413, 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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