A non-perturbative solution of the zero-dimensional λφ4 field theory

We have done a study of the zero-dimensional λφ4 model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for Re(λ) > 0. Secondly, an analytical continuation of the partition function for Re(λ) < 0 is performed, and we obtain an expression defined in complex coupling constant plane λ, for |arg λ| < π. Consequently, the partition function understood as an analytic continuation is defined for all values of λ, except for a branch cut along the real negative λ axis. We also evaluate the partition function on perturbative grounds, using the Borel summation technique and we found that in the common domain of validity for Re(λ > 0, it coincides precisely with the exact expression. (author)