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We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
We extend the Born-Oppenheimer type of approximation scheme for the Wheeler-DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this…
The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which…
This essay presents an accessible introduction to the basic motivations to seek a quantum theory of gravity. It focuses on one approach- loop quantum gravity - as an example of the rich philosophical issues that arise when we try to combine…
Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly…
In most approaches to fundamental physics, spacetime symmetries are postulated a priori and then explicitly implemented in the theory. This includes Lorentz covariance in quantum field theory and diffeomorphism invariance in quantum…
In this paper, we consider the time-dependent Born-Oppenheimer approximation (BOA) of a classical quantum molecule involving a possibly large number of nuclei and electrons, described by a Schr\"odinger equation. In the spirit of Born and…
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…
The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantum General Relativity (QGR). The constructions of…
An analysis is given of the local phase space of gravity coupled to matter to second order in perturbation theory. Working in local regions with boundaries at finite distance, we identify matter, Coulomb, and additional boundary modes. The…
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints…
Quantum decoherence is the disappearance of simple phase relations within a discrete quantum system as a result of interactions with an environment. For many applications, the question is not necessarily how to avoid (inevitable)…
In this paper, we discuss the compatibility between the rotating-wave and the adiabatic approximations for controlled quantum systems. Although the paper focuses on applications to two-level quantum systems, the main results apply in higher…
Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical…
We present an analogue spacetime model that reproduces the salient features of the most common ansatz for quantum gravity phenomenology. We do this by investigating a system of two coupled Bose-Einstein condensates. This system can be tuned…
It is univocally anticipated that in a theory of quantum gravity, there exist quantum superpositions of semiclassical states of spacetime geometry. Such states could arise for example, from a source mass in a superposition of spatial…
In this paper explore the relation between covariant and canonical approaches to quantum gravity and $BF$ theory. We will focus on the dynamical triangulation and spin-foam models, which have in common that they can be defined in terms of…
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like…
This paper serves as a preparation of work that focuses on extracting cosmological sectors from Loop Quantum Gravity. We start with studying the extraction of subsystems from classical systems. A classical Hamiltonian system can be reduced…