Related papers: Background Independent Quantum Mechanics, Classica…
The recent debate on hyper-computation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics. We propose here the idea of geometry of effective physical process as the…
An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds.…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
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…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
Black Holes have always played a central role in investigations of quantum gravity. This includes both conceptual issues such as the role of classical singularities and information loss, and technical ones to probe the consistency of…
A brief review of various numerical techniques used in loop quantum cosmology and results is presented. These include the way extensive numerical simulations shed insights on the resolution of classical singularities, resulting in the key…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions.…
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
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…