Non-Commutative Renormalization

Rivasseau, Vincent

doi:10.1007/978-3-7643-7434-1_19

Cited by 65 publications

(81 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, if the slashed line separates the graph into two disconnected components the first vertex may either belong to the four point component (G 4 (1) in Fig. 18) or to the two point component (G 4 (2) in Fig. 18).…”

Section: Proof Of Theorem 51mentioning

confidence: 99%

“…But these effects compensate. Indeed the bare G 4 (2) term is the left generalized tadpole Σ − Σ R , hence…”

Section: Bare Identitymentioning

confidence: 99%

“…But there is also a maximal observable scale or "horizon" in the universe, not for fundamental but for practical reasons. The current distance from the Earth to the edge of the visible universe is about 46 billion light-years in any direction 2 . This translates into a comoving radius of the visible universe of about 4.4 10 26 meters, or more fundamentally 2.7 10 61 Planck lengths.…”

Section: Introductionmentioning

confidence: 99%

“…The geometric mean between the size of the (observable) universe and the Planck's length stands therefore around 10 −4 meters, about the size of an (arguably very small) ant. In [2], we proposed to call this the "antropic principle".…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Non-commutative Renormalization

Rivasseau

2007

Quantum Spaces

Self Cite

View full text Add to dashboard Cite

Abstract. A new version of scale analysis and renormalization theory has been found on the non-commutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on non-commutative than on ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore be an alternative to supersymmetry. We review this rapidly growing subject.

show abstract

Section: Proof Of Theorem 51mentioning

confidence: 99%

“…But these effects compensate. Indeed the bare G 4 (2) term is the left generalized tadpole Σ − Σ R , hence…”

Section: Bare Identitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Non-commutative Renormalization

Rivasseau

2007

Quantum Spaces

Self Cite

View full text Add to dashboard Cite

show abstract

“…The extensive study of noncommutative quantum field theories (NCQFT) that started about 15 years ago has undergone several twists since then (for motivations and an overview, we refer to the reviews [1][2][3]). Right from the start, different approaches were followed.…”

Section: Introductionmentioning

confidence: 99%

Divergences in Quantum Field Theory on the Noncommutative Two-Dimensional Minkowski Space with Grosse–Wulkenhaar Potential

Zahn

2011

Ann. Henri Poincaré

View full text Add to dashboard Cite

Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: in terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position space. In both settings, we find a new type of divergence in planar graphs. It is present at and above the self-dual point. This new kind of divergence might make the construction of a Minkowski space version of the Grosse-Wulkenhaar model impossible.

show abstract

The tensor track, III

Rivasseau

2013

Fortschritte der Physik

100

View full text Add to dashboard Cite

We provide an informal up-to-date review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion, Osterwalder-Schrader positivity...) which, while important for the tensor track program, are not detailed in the usual quantum gravity literature. We list open questions in the conclusion and provide a rather extended bibliography.

show abstract

Non-Commutative Renormalization

Abstract: We review the recent approach of Grosse and Wulkenhaar to the perturbative renormalization of non commutative field theory and suggest a related constructive program. This paper is dedicated to J. Bros on his 65th birthday.

Cited by 65 publications

References 17 publications

Non-commutative Renormalization

Non-commutative Renormalization

Divergences in Quantum Field Theory on the Noncommutative Two-Dimensional Minkowski Space with Grosse–Wulkenhaar Potential

The tensor track, III

Contact Info

Product

Resources

About