Related papers: Classical and quantum general relativity: a new pa…
The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
In this short survey paper, we discuss certain recent results in classical gravity. Our main attention is restricted to two topics: the positive mass conjecture and its extensions to the case with horizons, including the Penrose conjecture…
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
We study gauge and gravitational field theories in which the gauge fixing conditions are imposed as constraints on classical fields. Quantization of fluctuations can be performed in a BRST invariant manner, while the main novelty is that…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
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…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…