Quantum field theory on the degenerate Moyal space

被引：11
|
作者：
Grosse, Harald [1 ]
Vignes-Tourneret, Fabien [2 ]
机构：
[1] Univ Vienna, Fac Phys, Math Phys Grp, A-1090 Vienna, Austria
[2] Univ Lyon 1, Inst Camille Jordan, F-69622 Villeurbanne, France
来源：
JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2010年 / 4卷 / 04期
关键词：
Non-commutative geometry; quantum field theory; renormalization; Moyal space; NONCOMMUTATIVE PHI(3) MODEL; RENORMALIZATION; DIMENSIONS;
D O I：
10.4171/JNCG/66
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangian. Despite the apparent simplicity of the model, it raises several non-trivial questions. Our result is a first step towards the definition of renormalisable quantum field theories on a non-commutative Minkowski space.
引用
收藏
页码：555 / 576
页数：22
相关论文
共 50 条
  • [21] Conformal Symmetry in Field Theory and in Quantum Gravity
    Rachwal, Leslaw
    UNIVERSE, 2018, 4 (11)
  • [22] On the energy-momentum tensor in Moyal space
    Balasin, Herbert
    Blaschke, Daniel N.
    Gieres, Franois
    Schweda, Manfred
    EUROPEAN PHYSICAL JOURNAL C, 2015, 75 (06):
  • [23] Shuffling quantum field theory
    Kreimer, D
    LETTERS IN MATHEMATICAL PHYSICS, 2000, 51 (03) : 179 - 191
  • [24] Noncommutative quantum field theory
    Grosse, Harald
    Wulkenhaar, Raimar
    FORTSCHRITTE DER PHYSIK-PROGRESS OF PHYSICS, 2014, 62 (9-10): : 797 - 811
  • [25] The Wilsonian revolution in statistical mechanics and quantum field theory
    Mandal G.
    Resonance, 2017, 22 (1) : 15 - 36
  • [26] Loop quantum cosmology from group field theory
    Calcagni, Gianluca
    PHYSICAL REVIEW D, 2014, 90 (06):
  • [27] Shuffling Quantum Field Theory
    D. Kreimer
    Letters in Mathematical Physics, 2000, 51 : 179 - 191
  • [28] The State Space of Perturbative Quantum Field Theory in Curved Spacetimes
    S. Hollands
    W. Ruan
    Annales Henri Poincaré, 2002, 3 : 635 - 657
  • [29] Quantum conformal algebras and closed conformal field theory
    Anselmi, D
    NUCLEAR PHYSICS B, 1999, 554 (1-2) : 415 - 436
  • [30] PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE
    Sanchis-Lozano, Miguel-Angel
    Barbero G, J. Fernando
    Navarro-Salas, Jose
    INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2012, 27 (23):
12345