相关论文: Dynamical Quantum Geometry (DQG Programme)

When studying gauge theories in the presence of boundaries, local symmetry transformations are typically classified as gauge or physical depending on whether the associated charges vanish or not. Here, we propose that physical charges…

The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…

Important characteristics of the loop approach to quantum gravity are a specific choice of the algebra A of observables and of a representation of A on a measure space over the space of generalized connections. This representation is…

Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…

We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean…

The fundamental symmetries in gravity and gauge theories, formulated using differential forms, are gauge transformations and diffeomorphisms. These symmetries act in distinct ways on different dynamical fields. Yet, the commutator of these…

In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=\mathbb{C}^*$…

We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the…

In the first part of the thesis we focus on local symmetries. We review a self-consistent framework that we employed in order to discuss the dynamics of the theories of interest. Its merit lies in that we can make the symmetry group act…

As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism…

Quantifying quantum resources for simulating the fundamental forces of Nature is sensitive to the mapping of gauge fields onto finite quantum computational architectures. When locally truncating lattice gauge theories in the irreducible…

Quantum holonomy theory is a candidate for a non-perturbative theory of quantum gravity coupled to fermions. The theory is based on the QHD(M) algebra, which essentially encodes how matter degrees of freedom are moved on a three-dimensional…

In this paper we explore the physical consequences of assuming Weyl invariance of the laws of gravity from the classical standpoint exclusively. Actual Weyl invariance requires to replace the underlying Riemannian geometrical structure of…

We introduce a framework to define coalgebra and bialgebra structures on two-dimensional (2D) square lattices, extending the algebraic theory of Hopf algebras and quantum groups beyond the one-dimensional (1D) setting. Our construction is…

We analyze the perturbative implications of the most general high derivative approach to quantum gravity based on a diffeomorphism invariant local action. In particular, we consider the super-renormalizable case with a large number of…

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…

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 phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…

We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and…

A first attempt at adding matter degrees of freedom to the two-dimensional ``vacuum'' gravity model presented in gr-qc/9907071 is analyzed in this paper. Just as in the previous pure gravity case, quantum diffeomorphism operators…