#### DMCA

## are the vacuum expectation values of products of physical fields, and contain (2013)

### Citations

159 | From Perturbative to Constructive Renormalization,
- Rivasseau
- 1991
(Show Context)
Citation Context ... recipe to compute to arbitrary accuracy the physical quantities. In a deep sense it is not a theory at all. Therefore we need to extend perturbative renormalization into constructive renormalization =-=[1]-=-. Constructive renormalization considers as equally important the finiteness of the renormalized arbitrary coefficients of the perturbation series and the summability of the series. For the Fermionic ... |

44 |
forests and jungles: A botanical garden for cluster expansions
- Abdesselam, Rivasseau, et al.
- 1995
(Show Context)
Citation Context ...al explicit summation of the amplitudes of different orders. The method gives direct access to thermodynamic quantities such as connected functions, and requires only a single use of a forest formula =-=[11, 12]-=- to compute connected quantities. It is a definite improvement over cluster and Mayer expansions, which require to use twice such a formula. In this paper we include for the first time renormalization... |

39 | Effective action for the Yukawa2 quantum field theory, - Lesniewski - 1987 |

34 |
expansions and the Hamilton-Jacobi equation
- Brydges, Kennedy, et al.
- 1987
(Show Context)
Citation Context ...al explicit summation of the amplitudes of different orders. The method gives direct access to thermodynamic quantities such as connected functions, and requires only a single use of a forest formula =-=[11, 12]-=- to compute connected quantities. It is a definite improvement over cluster and Mayer expansions, which require to use twice such a formula. In this paper we include for the first time renormalization... |

20 |
Phase Space Cell Expansion and Borel Summability for the Euclidean phi**4 in Three-Dimensions Theory
- Magnen, Seneor
- 1977
(Show Context)
Citation Context ...ons occur only between these different orders. Also the best we can hope for is only Borel summability [4]. The standard techniques for proving such Borel summability are cluster and Mayer expansions =-=[5, 6]-=-. These methods require to divide the space into cubes. This decomposition seems odd since it breaks the rotation invariance of the theory. What’s more, the cluster expansion seems unsuited for non-lo... |

14 |
Decay properties and Borel summability for the Schwinger functions
- Eckmann, Magnen, et al.
- 1975
(Show Context)
Citation Context ...ons occur only between these different orders. Also the best we can hope for is only Borel summability [4]. The standard techniques for proving such Borel summability are cluster and Mayer expansions =-=[5, 6]-=-. These methods require to divide the space into cubes. This decomposition seems odd since it breaks the rotation invariance of the theory. What’s more, the cluster expansion seems unsuited for non-lo... |

9 |
An Improvement Of Watson’s Theorem On
- Sokal
- 1980
(Show Context)
Citation Context ... condense. We need to combine amplitudes from infinitely many different orders, as the compensations occur only between these different orders. Also the best we can hope for is only Borel summability =-=[4]-=-. The standard techniques for proving such Borel summability are cluster and Mayer expansions [5, 6]. These methods require to divide the space into cubes. This decomposition seems odd since it breaks... |

8 | Loop Vertex Expansion for Φ2k Theory in Zero Dimension
- Rivasseau, Wang
(Show Context)
Citation Context ...nsuited for non-local theories, for example, noncommutative QFTs like the Grosse-Wulkenhaar model. Recently a new constructive Bosonic method has been invented, namely the loop vertex expansion (LVE) =-=[7, 8, 9, 10]-=-. In this method the role of 2 vertices and propagators is exchanged and one gets a natural explicit summation of the amplitudes of different orders. The method gives direct access to thermodynamic qu... |

6 |
Constructive matrix theory,” JHEP 0709
- Rivasseau
- 2007
(Show Context)
Citation Context ...nsuited for non-local theories, for example, noncommutative QFTs like the Grosse-Wulkenhaar model. Recently a new constructive Bosonic method has been invented, namely the loop vertex expansion (LVE) =-=[7, 8, 9, 10]-=-. In this method the role of 2 vertices and propagators is exchanged and one gets a natural explicit summation of the amplitudes of different orders. The method gives direct access to thermodynamic qu... |

6 | Constructive field theory without tears - Magnen, Rivasseau - 2008 |

3 | How are Feynman graphs resumed by the Loop Vertex Expansion?”, arXiv:1006.4617 [math-ph
- Rivasseau, Wang
(Show Context)
Citation Context ...nsuited for non-local theories, for example, noncommutative QFTs like the Grosse-Wulkenhaar model. Recently a new constructive Bosonic method has been invented, namely the loop vertex expansion (LVE) =-=[7, 8, 9, 10]-=-. In this method the role of 2 vertices and propagators is exchanged and one gets a natural explicit summation of the amplitudes of different orders. The method gives direct access to thermodynamic qu... |

2 |
Explicit fermionic tree expansions arXiv:cond-mat/9712055
- Abdesselam, Rivasseau
- 1998
(Show Context)
Citation Context ... of the renormalized arbitrary coefficients of the perturbation series and the summability of the series. For the Fermionic case, the summation of the series is easier thanks to the Pauli’s principle =-=[2, 3]-=-, which translates into compensations between graphs within a given order of perturbation theory. But the Bosonic case is much harder, as Bosons can condense. We need to combine amplitudes from infini... |