Corrected Loop Vertex Expansion for Phi42 Theory

This paper is an extended erratum to J. Math. Phys.53, 042302 (2012) and arXiv:1104.3443, in which the classic construction and Borel summability of the phi^4_2 Euclidean quantum field theory was revisited combining a multi-scale analysis with the constructive method called Loop Vertex Expansion (LVE). Unfortunately we discovered an important error in the method of J. Math. Phys.53, 042302 (2012). We explain the mistake, and provide a new, correct construction of the phi^4_2 theory according to the LVE.

[1]  G. Slade,et al.  A Renormalisation Group Method. V. A Single Renormalisation Group Step , 2014, 1403.7256.

[2]  G. Slade,et al.  A Renormalisation Group Method. IV. Stability Analysis , 2014, 1403.7255.

[3]  G. Slade,et al.  A Renormalisation Group Method. II. Approximation by Local Polynomials , 2014, 1403.7253.

[4]  G. Slade,et al.  A Renormalisation Group Method. III. Perturbative Analysis , 2014, 1403.7252.

[5]  G. Slade,et al.  A Renormalisation Group Method. I. Gaussian Integration and Normed Algebras , 2014, 1403.7244.

[6]  V. Rivasseau,et al.  Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions , 2014, Communications in Mathematical Physics.

[7]  V. Rivasseau,et al.  Borel summability and the non perturbative $1/N$ expansion of arbitrary quartic tensor models , 2014 .

[8]  R. Gurau.  The 1/N Expansion of Tensor Models Beyond Perturbation Theory , 2013, 1304.2666.

[9]  V. Rivasseau,et al.  The Multiscale Loop Vertex Expansion , 2013, 1312.7226.

[10]  V. Rivasseau,et al.  How to Resum Feynman Graphs , 2013, 1304.5913.

[11]  V. Rivasseau,et al.  Constructive renormalization for Φ24 theory with loop vertex expansion , 2011, 1104.3443.

[12]  Joseph Ben Geloun,et al.  A Renormalizable 4-Dimensional Tensor Field Theory , 2011, 1111.4997.

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

[14]  M. Smerlak,et al.  Scaling behavior of three-dimensional group field theory , 2009, 0906.5477.

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

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

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

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

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

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

[21]  J. Glimm,et al.  The Particle Structure of the Weakly Coupled P(φ)2 Model and Other Applications of High Temperature Expansions: Part II. The Cluster Expansion , 1985 .

[22]  J. Glimm,et al.  Quantum Physics: A Functional Integral Point of View , 1981 .

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

[24]  J. Glimm,et al.  The Particle Structure of the Weakly Coupled P(φ)2 Model and Other Applications of High Temperature Expansions , 1973 .