Related papers: Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC
The operator algebraic framework plays an important role in mathematical physics. Many different operator algebras exist for example for a theory of quantum mechanics. In Loop Quantum Gravity only two algebras have been introduced until…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques…
This article summarizes a new approach to quantum gravity based on the concepts of modular spacetime, Born geometry, and metastring theory and their applications to quantum gravity phenomenology. In particular, we discuss a new…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…
An introduction is given to discussions on the possiblity of fabricating spacetime geometries allowing time-travel scenarios with the help of matter possessing typically quantum features. Those scenarios are considered in the framework of…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
A theoretical framework based on a simple quasi-number algebra is investigated in a treatment of space-time and gravity.
Any acceptable quantum gravity theory must allow us to recover the classical spacetime in the appropriate limit. Moreover, the spacetime geometrical notions should be intrinsically tied to the behavior of the matter that probes them. We…
Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
A new direction to understand gravity has recently been explored by considering classical gravity to be a derived interaction from an underlying theory. This underlying theory would involve new degrees of freedom at a deeper level and it…
One of the most important issues in quantum gravity is to identify its semi-classical regime. First the issue is to define for we mean by a semi-classical theory of quantum gravity, then we would like to use it to extract physical…
Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Besides the purely digital or analog interpretation of reality there is a third possibility which incorporates important aspects of both. This is the cyclic formulation of elementary systems, in which elementary particles are represented as…
The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…