Related papers: Noncommutative Spacetime and Quantum Mechanics
We introduce a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in…
The purpose of this Chapter is to give a general introduction and status review on the perturbative approach to quantum gravity (QG). This text is a modified version of the corresponding chapters of Part II of the recent textbook on quantum…
We review the application of the loop representation to gauge theories and general relativity. The emphasis lies on exhibiting the loop calculus techniques, and their application to the canonical quantization. We discuss the role that knot…
We address gauge invariance in the statistical mechanics of quantum many-body systems. The gauge transformation acts on the position and momentum degrees of freedom and it is represented by a quantum shifting superoperator that maps quantum…
These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
The different roles and natures of spacetime appearing in a quantum field theory and in classical physics are analyzed implying that a quantum theory of gravitation is not necessarily a quantum theory of curved spacetime. Developing an…
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local…
We study the problem of gauge-invariance and gauge-dependence in one-loop quantum cosmology. We formulate some requirements which should be satisfied by boundary conditions in order to give gauge-independent path integral. The case of QED…
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
The paper is the second part of the work devoted to the problem of time in quantum cosmology. Here we consider in detail two approaches within the scope of Feynman path integration scheme: The first, by Simeone and collaborators, is…
In the present work, we study the noncommutative version of a quantum cosmology model. The model has a Friedmann-Robertson-Walker geometry, the matter content is a radiative perfect fluid and the spatial sections have positive constant…
Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows…
This study introduces the quantum force wave equation (QFWE) as a general theory of quantum forces, a novel framework that redefines quantum forces as emergent phenomena arising from the interaction between quantum particles and curved…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…