Related papers: Integration on the space of Connections Modulo Gau…
We show the inconsistency of the argument linking the integral quantum Hall effect to gauge invariance. The inconsistency mainly consists of equating gauge and real vector potential transformations for a particular system geometry. Correct…
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…
Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We rederive the recently introduced $N=2$ topological gauge theories, representing the Euler characteristic of moduli spaces ${\cal M}$ of connections, from supersymmetric quantum mechanics on the infinite dimensional spaces ${\cal A}/{\cal…
We discuss and review in this chapter the developing field of research of quantum simulation of gauge theories with ultracold atoms.
I review recent progress in understanding non-perturbative aspects of string theory, quantum gravity and non-commutative geometry using lattice methods.
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…
This is the introduction to the collection of review articles "Exact results on N=2 supersymmetric gauge theories". The first three sections are intended to give a general overview over the physical motivations behind this direction of…
We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a…
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or…
The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level,…
Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e.…
We complete the process of classifying all supersymmetric theories with quantum modified moduli. We present all the supersymmetric gauge theories based on a simple orthogonal or exceptional group that exhibit a quantum modified moduli…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…
First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These…
We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the…
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant…