相关论文: Why Renormalizable NonCommutative Quantum Field Th…

Constructing renormalizable models on non-commutative spaces constitutes a big challenge. Only few examples of renormalizable theories are known, such as the scalar Grosse-Wulkenhaar model. Gauge fields are even more difficult, since new…

The first renormalisable quantum field theories on non-commutative space have been found recently. We review this rapidly growing subject.

We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative…

We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.

We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the…

Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…

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…

In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…

We discuss some properties of noncommutative supersymmetric field theories which do not involve gauge fields. We concentrate on the renormalizability issue of these theories.

We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the…

Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type…

We review two different noncommutative gauge models generalizing approaches which lead to renormalizable scalar quantum field theories. One of them implements the crucial IR damping of the gauge field propagator in the so-called ``soft…

This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…

We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in…

Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…

Quantum field theory has been shown recently renormalizable on flat Moyal space and better behaved than on ordinary space-time. Some models at least should be completely finite, even beyond perturbation theory. In this paper a first step is…

In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel…

We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…