In quantum field theory, fields undergo quantum fluctuations. A reasonably clear distinction can be made between quantum fluctuations and thermal fluctuations of a quantum field (at least for a free field; for interacting fields, renormalization substantially complicates matters). An illustration of this distinction can be seen by considering quantum and classical Klein-Gordon fields: For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration φ t ( x ) {\displaystyle {\displaystyle \varphi _{t}(x)}} at a time t in terms of its Fourier transform φ ~ t ( k ) {\displaystyle {\displaystyle {\tilde {\varphi }}_{t}(k)}} to be