Path-integral quantization and cosmological particle production: An example

The Feynman path-integral method is applied to the quantization of a scalar field moving in a cosmological background spacetime. The method is illustrated by computing particle production from the vacuum in a spatially flat, Robertson-Walker spacetime with scale factor $R\mathrm{}\left(t\right)=t$. The result is a distribution of produced particle pairs which at large energies becomes a thermal distribution with a temperature $T=\frac{\hslash c}{\pi k_{B}R\mathrm{}\left(t\right)\mathrm{}}$. The relation to other methods of quantization is discussed.