相关论文: Matrix Models as Non-commutative Field Theories on…

We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…

We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally…

A general formalism is developed that allows the construction of a field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime (Poincar\' e group) is replaced by a quantum group. This…

Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend…

Many homogeneous, four-dimensional space-time geometries can be considered within real projective geometry, which yields a mathematically well-defined framework for their deformations and limits without the appearance of singularities.…

We study the noncommutative extensions of certain integrable field theories, namely the sine- and sinh-Gordon (sG and shG) models, and the U(N) principal chiral model (pcm). We argue that the Moyal deformations of the sG and shG models are…

Non-commutative (NC) field theories can be mapped onto twisted matrix models. This mapping enables their Monte Carlo simulation, where the large N limit of the matrix models describes the continuum limit of NC field theory. First we present…

We show that despite the inherent non-locality of quantum field theories on the Groenewold-Moyal (GM) plane, one can find a class of ${\bf C}$, ${\bf P}$, ${\bf T}$ and ${\bf CPT}$ invariant theories. In particular, these are theories…

This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…

In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…

Starting from square-integrable wave functions on a Lie group, we build an invertible Fourier transform mapping them on wave functions on the dual of the Lie algebra. This is a group-theoretic version of the map from position space to…

In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of `spin foam' is intended to serve as a similar picture for the quantum geometry of spacetime.…

Spin foam models are a new approach to a formulation of quantum gravity which is fully background independent, non-perturbative, and covariant, in the spirit of path integral formulations of quantum field theory. In this thesis we describe…

We link the notion causality with the orientation of the 2-complex on which spin foam models are based. We show that all current spin foam models are orientation-independent, pointing out the mathematical structure behind this independence.…

The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to…

In this review we discuss the global geometry of noncommutative field theories from a deformation point of view: The space-times under consideration are deformations of classical space-time manifolds using star products. Then matter fields…

We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field…

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…

In this paper, starting from pure group-theoretical point of view, we develop a regular approach to describing particles with different spins in the framework of a theory of scalar fields on the Poincare group. Such fields can be considered…

A number of background independent quantizations procedures have recently been employed in 4d nonperturbative quantum gravity. We investigate and illustrate these techniques and their relation in the context of a simple 2d topological…