Related papers: The QM/NCG Correspondence
In this thesis we study different aspects of noncommutativity in quantum mechanics, field theory and gravity. We give particular emphasis on the underlying symmetries of these theories. Deformations of usual symmetries like the external…
We review how the AdS/CFT correspondence is motivated within string theory, and discuss how it is generalized to gauge/gravity duality. In particular, we highlight the relation to quantum information theory by pointing out that the Fisher…
In the context of the AdS/CFT correspondence, an explicit relation between the physical degrees of freedom of 2+1d gravity and the stress tensor of 1+1d conformal field theory is exhibited. Gravity encodes thermodynamic state variables of…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is…
We examine the scaling of geodesic correlation functions in two-dimensional gravity and in spin systems coupled to gravity. The numerical data support the scaling hypothesis and indicate that the quantum geometry develops a non-perturbative…
We study the implications of a noncommutative geometry of the minisuperspace variables for the FRW universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
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…
We analyze the effects of the back reaction due to a conformal field theory (CFT) on a black hole spacetime with negative cosmological constant. We study the geometry numerically obtained by taking into account the energy momentum tensor of…
In a recent paper we have suggested that a formulation of quantum mechanics should exist, which does not require the concept of time, and that the appropriate mathematical language for such a formulation is noncommutative differential…
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do…
In this paper we use considerations of non-commutative geometry to deduce a model for QCD interactions. The model also explains within the same theoretical framework hitherto purely phenomenological characteristics of the quarks like their…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
In this paper we make an extensive description of quantum non-locality, one of the most intriguing and fascinating facets of quantum mechanics. After a general presentation of several studies on this subject, we consider if quantum…
Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.
This article gives a comprehensive description of the fractal geometry of conformally-invariant (CI) scaling curves, in the plane or half-plane. It focuses on deriving critical exponents associated with interacting random paths, by…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Parallels between the measurement problem in quantum mechanics and the black hole information loss problem in quantum gravity are exhibited and then the attempted resolution of the latter in terms of the gauge/gravity duality is extended to…