相关论文: Noncommutative effective field theories and the la…
We address the treatment of gauge theories within the framework that is formed from combining the machinery of noncommutative symplectic geometry, as introduced by Kontsevich, with Costello's approach to effective gauge field theories…
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
We elaborate on the dynamics of noncommutative two-dimensional gauge field theories. We consider U(N) gauge theories with fermions in either the fundamental or the adjoint representation. Noncommutativity leads to a rather non-trivial…
We consider Yang-Mills theories formulated on a non-commutative space-time described by a space-time dependent anti-symmetric field $\theta^{\mu\nu}(x)$. Using Seiberg-Witten map techniques we derive the leading order operators for the…
The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of some of the mathematical results which…
We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the…
We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a…
The 1/N expansion in quantum field theory is formulated within an algebraic framework. For a scalar field taking values in the $N$ by $N$ hermitian matrices, we rigorously construct the gauge invariant interacting quantum field operators in…
We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary…
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…
The Connes and Lott reformulation of the strong and electroweak model represents a promising application of noncommutative geometry. In this scheme the Higgs field naturally appears in the theory as a particular `gauge boson', connected to…
Noncommutative geometry is based on an idea that an associative algebra can be regarded as "an algebra of functions on a noncommutative space". The major contribution to noncommutative geometry was made by A. Connes, who, in particular,…
We examine the issue of renormalizability of asymptotically free field theories on non-commutative spaces. As an example, we solve the non-commutative O(N) invariant Gross-Neveu model at large N. On commutative space this is a…
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite…
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open…
We assume that the noncommutativity starts to be visible continuously from a scale $\Lambda_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $\phi^{4}$ and $\phi^{3}$ theories from a Wilsonian…
We show that the classical non-abelian pure Chern-Simons action is related to nonrelativistic models in (2+1)-dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to…
We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In…