Related papers: Observability and Geometry in Three dimensional qu…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

We investigate the relation between measurements and the physical observables for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with vanishing cosmological constant. By considering an observer who emits lightrays that…

A new approach to a unified theory of quantum gravity based on noncommutative geometry and canonical quantum gravity is presented. The approach is built around a *-algebra generated by local holonomy-diffeomorphisms on a 3-manifold and a…

In a companion paper we studied field theory in the presence of a physical observer with quantum dynamics. Here we describe the most striking consequence of this assumption: new gauge and diff anomalies arise. The relevant cocycles depend…

It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for…

We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…

Describing dynamics in a gravitational universe with positive cosmological constant, such as de Sitter space, is a conceptually challenging problem. We propose a principle for constructing a quantum system that can potentially be used to…

We combine the "evolving constants" approach to the construction of observables in canonical quantum gravity with the Page--Wootters formulation of quantum mechanics with a relational time for generally covariant systems. This overcomes the…

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…

We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…

Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using…

In a previous paper, we showed how to use the techniques of the group of loops to formulate the loop approach to gravity proposed by Mandelstam in the 1960's. Those techniques allow to overcome some of the difficulties that had been…

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy…

We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…

Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…

We review the motivation, construction and physical interpretation of a semi-finite spectral triple obtained through a rearrangement of central elements of loop quantum gravity. The triple is based on a countable set of oriented graphs and…

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…

The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…