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2012

Degenerate noncommutativity

Grosse, Harald, Wohlgenannt, Michael

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We study a renormalizable four dimensional model with two deformed quantized space directions.

A one-loop renormalization is performed explicitly.
The Euclidean model is connected to the Minkowski version via an analytic continuation.
At a special value of the parameters a nontrivial fixed point of the renormalization group occurs.

Degenerate noncommutativity · Around

Built on

J. M. Gracia-Bondia and J. C. Varilly, “Algebras of distributions suitable for phase space quantum mechanics. 1,” J. Math. Phys
1988
Earlier work this paper cites.
H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} theory on noncommutative ℝ 2 \mathbb{R}^{2} in the matrix base,” JHEP
2003
Earlier work this paper cites.
H. Grosse and R. Wulkenhaar, “The β \beta -function in duality-covariant noncommutative ϕ 4 \phi^{4} theory,” Eur. Phys. J
2004
Earlier work this paper cites.
H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} theory on noncommutative ℝ 4 \mathbb{R}^{4} in the matrix base,” Commun. Math. Phys
2005
Earlier work this paper cites.

Similar

F. Vignes-Tourneret, “Renormalization of the orientable non-commutative Gross-Neveu model,” Annales Henri Poincare
2007
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R. Gurau, J. Magnen, V. Rivasseau, and A. Tanasa, “A translation-invariant renormalizable non-commutative scalar model,” Commun. Math. Phys
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2009
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A. Fischer and R. J. Szabo, “Duality covariant quantum field theory on noncommutative Minkowski space,” JHEP
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2009
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J. Zahn, “Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential,” arXiv:1005.0541 [hep-th]
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D. Bahns, “The ultraviolet infrared mixing problem on the noncommutative Moyal space,” arXiv:1012.3707 [hep-th]
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H. Grosse, G. Lechner, T. Ludwig, and R. Verch, “Wick rotation for quantum field theories on degenerate Moyal space(-time),” arXiv:1111.6856 [hep-th]
Original
Cited in the paper.
V. Rivasseau, “Non-commutative renormalization,” arXiv:0705.0705 [hep-th]
Original
Cited in the paper.

Then

H. Grosse and F. Vignes-Tourneret, “Quantum field theory on the degenerate Moyal space,” J. Noncommut. Geom
Original
2010
Later among the works it cites.
D. Bahns, “Schwinger functions in noncommutative quantum field theory,” Annales Henri Poincare
Original
2010
Later among the works it cites.
A. Fischer and R. J. Szabo, “Propagators and Matrix Basis on Noncommutative Minkowski Space,” Phys. Rev
Original
2011
Later among the works it cites.

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