- #1
spookyfish
- 53
- 0
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].
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].