Constructive renormalization for Φ24 theory with loop vertex expansion

In this paper, we construct the two-dimensional Euclidean ϕ4 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.

[1]  Zhituo Wang.  Construction of 2-dimensional Grosse-Wulkenhaar Model , 2011 .

[2]  J. Zahn.  Divergences in Quantum Field Theory on the Noncommutative Two-Dimensional Minkowski Space with Grosse–Wulkenhaar Potential , 2010, 1005.0541.

[3]  V. Rivasseau,et al.  How are Feynman graphs resummed by the Loop Vertex Expansion , 2010, 1006.4617.

[4]  V. Rivasseau,et al.  Loop Vertex Expansion for Phi^2k Theory in Zero Dimension , 2010, 1003.1037.

[5]  H. Grosse,et al.  Progress in solving a noncommutative quantum field theory in four dimensions , 2009, 0909.1389.

[6]  V. Rivasseau,et al.  Constructive ϕ4 Field Theory without Tears , 2007, 0706.2457.

[7]  V. Rivasseau.  Constructive matrix theory , 2007, 0706.1224.

[8]  M. Disertori,et al.  Vanishing of beta function of non-commutative Φ 4 4 theory to all orders , 2006, hep-th/0612251.

[9]  V. Rivasseau,et al.  Renormalisation of Noncommutative ϕ4-Theory by Multi-Scale Analysis , 2005, Communications in Mathematical Physics.

[10]  M. Disertori,et al.  Continuous Constructive Fermionic Renormalization , 1998, hep-th/9802145.

[11]  V. Rivasseau,et al.  Explicit Fermionic Tree Expansions , 1997, cond-mat/9712055.

[12]  V. Rivasseau,et al.  Trees, forests and jungles: a botanical garden for cluster expansions , 1994, hep-th/9409094.

[13]  Vincent Rivasseau,et al.  From Perturbative to Constructive Renormalization , 1991 .

[14]  A. Leśniewski.  Effective action for the Yukawa-2 quantum field theory , 1987 .

[15]  T. Kennedy,et al.  Mayer expansions and the Hamilton-Jacobi equation , 1987 .

[16]  Alan D. Sokal,et al.  An improvement of Watson’s theorem on Borel summability , 1980 .

[17]  R. Sénéor,et al.  Phase space cell expansion and borel summability for the Euclidean φ34 theory , 1977 .

[18]  R. Sénéor,et al.  Decay properties and borel summability for the Schwinger functions inP(Φ)2 theories , 1975 .

[19]  Barry Simon,et al.  The P(φ)[2] Euclidean (quantum) field theory , 1974 .