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We give a brief review of the problem of quantum gravity. After the discussion of the nonrenormalizability of general relativity, we briefly mention the main research directions which aim to resolve this problem. Our attention then focuses…
The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We…
We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum…
Recently we have discussed a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so…
We discuss recent progress in Tensor Lattice Field Theory and economical, symmetry preserving, truncations suitable for quantum computations or simulations. We focus on spin and gauge models with continuous Abelian symmetries such as the…
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor ordering choices ensuring in an anomaly free quantum constraint…
We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal…
We give a brief introduction to matrix models and the group field theory (GFT) formalism as realizations of the idea of a third quantization of gravity, and present in some more detail the idea and basic features of a continuum third…
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum gravity and is carried out at the metric…
In this paper, we address the problem of the dynamics in three dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert…
We study the quantization of spherically symmetric vacuum spacetimes within loop quantum gravity. In particular, we give additional details about our previous work in which we showed that one could complete the quantization the model and…
Loop Quantum Gravity is now a well established approach to quantum gravity. One of the main challenges still faced by the theory is constructing a consistent dynamics which would lead back to the standard dynamics of the gravitational field…
As a necessary step towards the extraction of realistic results from Loop Quantum Cosmology, we analyze the physical consequences of including inhomogeneities. We consider in detail the quantization of a gravitational model in vacuo which…
Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented bounded in one orientation, e.g., a…
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…
The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows to test loop quantum gravity in a large class of minisuperspaces and to investigate its features…
We present a new perspective on early cosmology based on Loop Quantum Gravity. We use projected spinnetworks, coherent states and spinfoam techniques, to implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Quantum Reduced Loop Gravity is a promising framework for linking Loop Quantum Gravity and the effective semiclassical dynamics of Loop Quantum Cosmology. We review its basic achievements and its main perspectives, outlining how it provides…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…