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Field mediated entanglement experiments probe the quantum superposition of macroscopically distinct field configurations. We show that this phenomenon can be described by using a transparent quantum field theoretical formulation of…
The presented paper is a review of papers on the microcosm physics geometrization in the last twenty years. These papers develop a new direction of the microcosm physics. It is so-called geometric paradigm, which is alternative to the…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
Quantum simulation is making a significant impact on scientific research. The prevailing tendency of the field is to build quantum simulators that get closer to real-world systems of interest, in particular electronic materials. However,…
Nonmagnetic and spherically symmetric dielectric material media are investigated in their generality as analogue models, in the domains of geometrical optics, for a few relevant static and spherically symmetric solutions of gravitation,…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
In this paper we construct a model for group field cosmology. The classical equations of motion for the non-interactive part of this model generate the Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic universe…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
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…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
We investigate the utility of geometric (Clifford) algebras (GA) methods in two specific applications to quantum information science. First, using the multiparticle spacetime algebra (MSTA, the geometric algebra of a relativistic…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…