Abstract
We develop a computationally tractable method for calculating correlation functions of the finite temperature trapped Bose gas that includes the effects of s-wave interactions. Our approach uses a classical field method to model the low energy modes and treats the high energy modes using a Hartree-Fock description. We present results of first and second order correlation functions, in position and momentum space, for an experimentally realistic system in the temperature range of 0.6T(c) to 1.0T(c). We also characterize the spatial coherence length of the system. Our theory should be applicable in the critical region where experiments are now able to measure first and second order correlations.