Constructive Renormalization for $\Phi^{4}_2$ Theory with Loop Vertex   Expansion
  In this paper we construct the 2 dimensional Euclidean $\phi^4$ quantum field theory using the method of loop vertex expansion. We reproduce the results of standard constructive theory, for example the Borel summability of the Schwinger functions in the coupling constant. Our method should be also suitable for the future construction of Grosse-Wulkenhaar models on non-commutative space-time. 
Vincent Rivasseau and Zhituo Wang
math-ph hep-th math.MP