- #1
pleasehelpmeno
- 154
- 0
Hi can I just check that i haven't done anyhting foolish here whe quantising the scalar field;
[itex]\ddot{\phi} - \frac{1}{a^2}\nabla \phi + 3H\dot{\phi} - 3\frac{H}{a^2}\nabla \phi + m^2 \phi[/itex]
with [itex]\phi = \int \frac{d^3 K}{(2\pi)^{\frac{3}{2}}}(\chi \exp(+ikx) +\chi \dagger \exp(-ikx))[/itex]
then all one does is sub [itex]\phi = (\chi \exp(+ikx) +\chi \dagger \exp(-ikx))[/itex] into the top expression and replace [itex]-ik\chi \dagger\exp(-ikx)[/itex] with [itex]-ik\chi \exp(+ikx[/itex] so that it cancels.
thx
[itex]\ddot{\phi} - \frac{1}{a^2}\nabla \phi + 3H\dot{\phi} - 3\frac{H}{a^2}\nabla \phi + m^2 \phi[/itex]
with [itex]\phi = \int \frac{d^3 K}{(2\pi)^{\frac{3}{2}}}(\chi \exp(+ikx) +\chi \dagger \exp(-ikx))[/itex]
then all one does is sub [itex]\phi = (\chi \exp(+ikx) +\chi \dagger \exp(-ikx))[/itex] into the top expression and replace [itex]-ik\chi \dagger\exp(-ikx)[/itex] with [itex]-ik\chi \exp(+ikx[/itex] so that it cancels.
thx