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