论文信息 - Renormalization of Non-Commutative Φ_4 Field Theory in x Space

Renormalization of Non-Commutative Φ_4 Field Theory in x Space

In this paper we provide a new proof that the Grosse-Wulkenhaar noncommutative scalar Φ4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).

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

[2] Non-commutative Renormalization , 2004, 0705.0705.

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

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

[5] Fabien Vignes-Tourneret,et al. Propagators for Noncommutative Field Theories , 2005 .

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

[7] Grosse,et al. The β-function in duality-covariant noncommutative φ 4-theory , 2008 .

[8] Michael R. Douglas,et al. Noncommutative field theory , 2001 .

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

[10] Giovanni Gallavotti,et al. Renormalization theory in four-dimensional scalar fields (I) , 1985 .

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

[12] Interacting fermions on non-commutative spaces: exactly solvable quantum field theories in 2n+1 dimensions , 2002, hep-th/0205287.

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

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

[15] Convergence theorem for non-commutative Feynman graphs and renormalization , 2000, hep-th/0008090.