Constructive Tensor Field Theory

2016/03/31 by Vincent Rivasseau, Universit&, #233 +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Black Holes and Theoretical Physics #Classical field theory #Computer science #Constructive #Exact solutions in general relativity #Field (mathematics) #Field theory (psychology) #General relativity #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Noncommutative and Quantum Gravity Theories #Physics #Programming language #Pure mathematics #Symmetric tensor #Tensor (intrinsic definition) #Tensor calculus #Tensor contraction #Tensor field #Tensor product #Theoretical physics #math-ph #math.MP

paper · pdf · doi:10.3842/sigma.2016.085

published as SIGMA 12 (2016), 085, 31 pages · arXiv admin note: text overlap with arXiv:1401.5003

arxiv created 2016/08/22 · openalex publication_date 2016/08/22 · arxiv updated 2016/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.

Citations

• Renormalization: an advanced overview
• On the shortest spanning subtree of a graph and the traveling salesman problem
• Scaling behavior of three-dimensional group field theory
• Colored Group Field Theory
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Renormalization of a SU(2) Tensorial Group Field Theory in Three Dimensions
• Note on the Intermediate Field Representation of Phi²k Theory in Zero Dimension

Cited by

• Topology in colored tensor models via crystallization theory