A Translation-Invariant Renormalizable Non-Commutative Scalar Model

In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders in perturbation theory.

[1]  A. U.S.  Quantum Hall Physics Equals Noncommutative Field Theory , 2001 .

[2]  Fabien Vignes-Tourneret,et al.  Renormalisation of Noncommutative ϕ4-Theory by Multi-Scale Analysis , 2006 .

[3]  H. Grosse,et al.  Renormalisation of ϕ4-Theory on Noncommutative ℝ4 in the Matrix Base , 2004, hep-th/0401128.

[4]  P. Bieliavsky.  Deformation quantization for actions of the affine group , 2007, 0709.1110.

[5]  Fabien Vignes-Tourneret.  Renormalization of the Orientable Non-commutative Gross–Neveu Model , 2006 .

[6]  A. Connes,et al.  Géométrie non commutative , 1990 .

[7]  D. Bahns.  The shuffle Hopf algebra and quasiplanar Wick products , 2007, 0710.2787.

[8]  T. Filk.  Divergencies in a field theory on quantum space , 1996 .

[9]  A. Connes.  Non-commutative geometry and physics , 1995 .

[10]  H. Grosse,et al.  8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory , 2007, 0709.0095.

[11]  Fabien Vignes-Tourneret,et al.  Renormalization of Non-Commutative $$\Phi^4_4$$ Field Theory in x Space , 2006 .

[12]  Shiraz Minwalla,et al.  Noncommutative perturbative dynamics , 2000 .

[13]  V. Rivasseau,et al.  Non-Commutative Complete Mellin Representation for Feynman Amplitudes , 2007, Letters in Mathematical Physics.

[14]  Wei He,et al.  Quantum spaces , 2010 .

[15]  The $\beta$-function in duality-covariant non-commutative $\phi^4$-theory , 2004, hep-th/0402093.

[16]  Noncommutative induced gauge theory , 2007, hep-th/0703075.

[17]  M. Raamsdonk,et al.  Quantum Hall Physics = Noncommutative Field Theory , 2001, hep-th/0103179.

[18]  Robert C. Helling,et al.  Macroscopic screening of 1/rpotentials from UV/IR-mixing , 2007, Journal of High Energy Physics.

[19]  Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory , 2001, hep-th/0106011.

[20]  A. Tanasa,et al.  Dimensional Regularization and Renormalization of Non-Commutative Quantum Field Theory , 2007, 0706.1147.

[21]  Nathan Seiberg,et al.  String theory and noncommutative geometry , 1999 .

[22]  A. Tanasa,et al.  Vacuum configurations for renormalizable non-commutative scalar models , 2007, 0709.3950.

[23]  Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces , 2003, hep-th/0308043.

[24]  Adrian Tanasa,et al.  Hopf algebra of non-commutative field theory , 2007, 0707.4143.

[25]  Alain Connes,et al.  Noncommutative Geometry and Matrix Theory: Compactification on Tori , 1997, hep-th/9711162.

[26]  Power-Counting Theorem for Non-Local Matrix Models and Renormalisation , 2003, hep-th/0305066.

[27]  H. Snyder,et al.  Quantized Space-Time , 1947 .

[28]  The Quantum Hall Fluid and Non-Commutative Chern Simons Theory , 2001, hep-th/0101029.

[29]  V. Rivasseau,et al.  Parametric Representation of “Covariant” Noncommutative QFT Models , 2007, math-ph/0701034.