Related papers: Volume and Quantizations
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these…
We investigate the quantitative relationship between operator spreading and classical information propagation in quantum systems. Focusing on a bi-partite quantum channel, we derive new upper and lower bounds on the Holevo capacity, a…
We provide an overview of the de Broglie-Bohm pilot-wave formulation of quantum mechanics, emphasising its applications to field theory, high-energy physics, gravitation, and cosmology.
When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does…
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only…
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the…
The general aim of this paper is to extend the Modal-Hamiltonian interpretation of quantum mechanics to the case of relativistic quantum mechanics with gauge U(1) elds. In this case we propose that the actual- valued observables are the…
In this paper we introduce the n-dimensional hypersurface quantum volume operator by using the n-dimensional holonomy variation formula. Instead of trying to construct the n-dimensional hypersurface volume operator by using the n-1…
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
Through the analyses of volume-forms in differentiable manifolds, it is shown that the usual way of defining minimal action principles for field theory on curved space-times is not appropriate on non-riemannian manifolds. An alternative…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
The primary purpose of this paper is to investigate the question of invertibility of the sum of operators. The setting is bounded and unbounded linear operators. Some interesting examples and consequences are given. As an illustrative…
This is the second paper in the series to introduce a graphical method to loop quantum gravity. We employ the graphical method as a powerful tool to calculate the actions of the Euclidean Hamiltonian constraint operator and the so-called…
A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…