Related papers: Non-commutative quantum geometric data in group fi…
We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…
Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in…
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups,…
We present a general framework for Matrix theory compactified on a quotient space R^n/G, with G a discrete group of Euclidean motions in R^n. The general solution to the quotient conditions gives a gauge theory on a noncommutative space. We…
We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the…
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phase and the logarithm of its amplitude. Equations Doebner and…
We introduce the group field theory formalism for quantum gravity, mainly from the point of view of loop quantum gravity, stressing its promising aspects. We outline the foundations of the formalism, survey recent results and offer a…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case ($q \rightarrow 1$ limit). The Lie derivative and the contraction operator on forms and…
These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
Group field theories are quantum field theories built on groups. They can be seen as a tool to generate topological state-sums or quantum gravity models. For four dimensional manifolds, different arguments have pointed towards 2-groups…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
Noncommutative field theory (NCFT) is an extension of quantum field theory (QFT) that redefines spacetime, replacing commuting coordinates with a noncommutative structure. This shift fundamentally alters the way fields, interactions, and…