Constructive Renormalization for ${\Phi }_2^4$ Theory with Loop Vertex Expansion

Abstract

In this paper we construct the 2 dimensional Euclidean ${\varphi }^4$ 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.

The paper has been withdrawn because it contained some mistakes found by the authors themselves and which they corrected in the new version arXiv:1406.7428

References in corpus (7)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Constructive ${\varphi }^4$ field theory without tears
• Loop Vertex Expansion for Phi^2k Theory in Zero Dimension
• Constructive Matrix Theory
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Cited by in corpus (7)

• Double Scaling in Tensor Models with a Quartic Interaction
• The Tensor Track, III
• How to Resum Feynman Graphs
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• Particle Physics from Almost Commutative Spacetimes
• Generalized constructive tree weights
• A path-integral analysis of interacting Bose gases and loop gases