Vincent Rivasseau, Zhituo Wang
Published 2011-04-18, updated 2014-07-01Version 3
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.
Comments: The paper has been withdrawn because it contained some mistakes found by the authors themselves and which they corrected in the new version arXiv:1406.7428
Journal: J. Math. Phys. 53, 042302 (2012)
On the representation of effective quantum field theories
Existence of the Bogoliubov S(g) operator for the $(:φ^4:)_2$ quantum field theory
How are Feynman graphs resumed by the Loop Vertex Expansion?
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