Related papers: C*-algebras of Holonomy-Diffeomorphisms & Quantum …
We investigate the representation of diffeomorphisms in Connes' Spectral Triples formalism. By encoding the metric and spin structure in a moving frame, it is shown on the paradigmatic example of spin semi-Riemannian manifolds that the…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
Loop quantum gravity corrections, in the presence of inhomogeneities, can lead to a deformed constraint algebra. Such a deformation implies that the effective theory is no longer generally covariant. As a consequence, the geometrical…
I construct a finite-dimensional quantum theory from general relativity by a homotopy method. Its quantum history is made up of at least two levels of fermionic elements. Its unitary group has the diffeomorphism group as singular limit. Its…
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation…
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin…
We postulate that the fundamental principles of Quantum Gravity are diffeomorphism symmetry, unitarity, and locality. Local observables are compatible with diffeomorphism symmetry in the presence of diff anomalies, which modify the symmetry…
We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal…
A simple diffeomorphism invariant theory of connections with the non-compact structure group R of real numbers is quantized. The theory is defined on a four-dimensional 'space-time' by an action resembling closely the self-dual Plebanski…
We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras…
The progress of noncommutative geometry has been crucially influenced, from the beginning, by quantum physics: we review this development in recent years. The Standard Model, with its central role for the Dirac operator, led to several…
Inspired by previous work in 2+1 dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and…
We quantize spherically symmetric vacuum gravity without gauge fixing the diffeomorphism constraint. Through a rescaling, we make the algebra of Hamiltonian constraints Abelian and therefore the constraint algebra is a true Lie algebra.…
This is the first of two papers which study the behavior of the SU(2) holonomies of loop quantum gravity (LQG), when they are acted upon by a unidirectional, plane gravity wave. Initially, the LQG flux-holonomy variables are treated as…
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…
Holonomy algebras arise naturally in the classical description of Yang-Mills fields and gravity, and it has been suggested, at a heuristic level, that they may also play an important role in a non-perturbative treatment of the quantum…
We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…
Solutions to a scalar-tensor (dilaton) quantum gravity theory, interacting with quantized matter, are described. Dirac quantization is frustrated by quantal anomalies in the constraint algebra. Progress is made only after the…
We consider a simplified model of double scaled SYK (DSSYK) in which the Hamiltonian is the position operator of the Harmonic oscillator. This model captures the high temperature limit of DSSYK but could also be defined as a quantum theory…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…