Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-09-23
Physica A292 (2001) 485-493
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, 2 figures
Scientific paper
10.1016/S0378-4371(00)00587-2
We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of the partition function for $Re(\lambda)<0$ is performed, and we obtain an expression defined in the complex coupling constant plane $\lambda$, for $|arg \lambda|<\pi$. Consequently, the partition function understood as an analytic continuation is defined for all values of $\lambda$, except for a branch cut along the real negative $\lambda$ 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 $Re(\lambda)>0$, it coincides precisely with the exact expression.
Malbouisson Adolfo P. C.
Portugal Renato
Svaiter Nami F.
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