  Complete information on the equilibrium behaviour and dynamics of a quantum
field theory (QFT) is provided by multipoint correlation functions. However,
their theoretical calculation is a challenging problem, even for exactly
solvable models. This has recently become an experimentally relevant problem,
due to progress in cold-atom experiments simulating QFT models and directly
measuring higher order correlations. Here we compute correlation functions of
the quantum sine-Gordon model, a prototype integrable model of central interest
from both theoretical and experimental points of view. Building upon the
so-called Truncated Conformal Space Approach, we numerically construct higher
order correlations in a system of finite size in various physical states of
experimental relevance, both in and out of equilibrium. We measure deviations
from Gaussianity due to the presence of interaction and analyse their
dependence on temperature, explaining the experimentally observed crossover
between Gaussian and non-Gaussian regimes. We find that correlations of excited
states are markedly different from the thermal case, which can be explained by
the integrability of the system. We also study dynamics after a quench,
observing the effects of the interaction on the time evolution of correlation
functions, their spatial dependence, and their non-Gaussianity as measured by
the kurtosis.
