Related papers: The projector on physical states in loop quantum g…
We present a generalization of the first-order formalism used to describe the dynamics of a classical system. The generalization is then applied to the first-order action that describes General Relativity. As a result we obtain equations…
A class of diffeomorphism invariant, physical observables, so-called astrometric observables, is introduced. A particularly simple example, the time delay, which expresses the difference between two initially synchronized proper time clocks…
In the search for a covariant formulation for Loop Quantum Gravity, spin foams have arised as the corresponding discrete space-time structure and, among the different models, the Barrett-Crane model seems the most promising. Here, we study…
We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the…
We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We show that the perturbation expansion of…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
A phenomenology for the deep spatial geometry of loop quantum gravity is introduced. In the context of a simple model, an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used to…
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization…
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…
Complex numbers are theoretically proved and experimentally confirmed as necessary in quantum mechanics and quantum information, and a resource theory of imaginarity of quantum states has been established. In this work, we establish a…
This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
A manifestly diffeomorphism-invariant approach to canonical quantum gravity requires to use composite operators. These can be considered to be bound states of matter and/or gravitons, intrinsically non-perturbative objects. An analytical…
We use the method of embedding a subsystem (i.e. its observable algebra) into a larger quantum system to extract a cosmological sector from full Loop Quantum Gravity. The application of this method provides a setting for a systematic study…
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
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…
We present and analyze a gauge-invariant quantum theory of the Friedmann-Robertson-Walker universe with dust. We construct the reduced phase space spanned by gauge-invariant quantities by using the so-called relational formalism at the…