Is This the Correct Method for Quantizing the Scalar Field?

[pleasehelpmeno]

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

 

[azntoon]

Yes, this is correct. You have correctly quantized the scalar field and replaced the derivatives with wavenumbers.