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This paper presents an overview of close parallels that exist between the theory of positive operator-valued measures (POVMs) associated with a separable Hilbert space and the theory of frames on that space, including its most important…
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…
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
We motivate and construct a mathematical theory for the separation of space and time in general relativity. The formalism only requires a single observer and an optional choice of reference frame at each instant. As the splitting is done…
In the framework of the Hartle-Hawking no-boundary proposal, we investigated quantum creation of the multidimensional universe with a cosmological constant ($\Lambda$) but without matter fields. We have found that the classical solutions of…
This article sheds new light on the problem of cosmological reduction in Loop Quantum Gravity. We critically analyze Quantum Reduced Loop Gravity -- an attempt to extract the cosmological sector of the full theory. We reconsider the…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
As gravity is a long-range force, one might a priori expect the Universe's global matter distribution to select a preferred rest frame for local gravitational physics. At the post-Newtonian approximation, two parameters suffice to describe…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
The saddle point approximation to formal quantum gravitational partition functions has yielded plausible computations of horizon entropy in various settings, but it stands on shaky ground. In this paper we visit some of that shaky ground,…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
Space-time measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about space-time is in fact an assertion…
Black holes in our Universe are rarely truly isolated, being instead embedded in astrophysical environments such as plasma or dark matter. A particularly intriguing possibility is that light scalar fields form bound states around black…
The phenomenon of half-spectral unidirectional invisibility is introduced for one-dimensional periodic optical structures with tailored real and imaginary refractive index distributions in a non-$\mathcal{PT}$-symmetric configuration. The…
Some preliminaries and basic facts regarding unbounded Wiener-Hopf operators (WH) are provided. WH with rational symbols are studied in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency…
We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…
We investigate the gravitational-wave background predicted by a two-scalar-field cosmological model that aims to unify primordial inflation with the dark sector, namely late-time dark energy and dark matter, in a single and self-consistent…