Related papers: Noncommutative Conformal Field Theory in the Twist…
We review basic notions and methods of noncommutative geometry and their applications to analysis and geometry on foliated manifolds.
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the…
A new method is developed for solving the conformally invariant integrals that arise in conformal field theories with a boundary. The presence of a boundary makes previous techniques for theories without a boundary less suitable. The method…
We investigate a conformal-like transformation for which the spacetime interval is invariant.
We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton…
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We write down scalar field theory and gauge theory on two-dimensional noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$ going to i) a…
Generators of the super-Poincar\'e algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the…
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly…
We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $\theta $ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and…
Application of the noncommutative geometry to several physical models is considered.
We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $\theta^{\mu\nu}$. In this case the…
A comprehensive introduction to two-dimensional conformal field theory is given.
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
Based on an argument for the noncommutativity of momenta in noncommutative directions, we arrive at a generalization of the ${\cal N}=1$ super $E^2$ algebra associated to the deformation of translations in a noncommutative Euclidean plane.…
Non-geometric string backgrounds were proposed to be related to a non-associative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…
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…