Related papers: Geometric Approach to Quantum Theory
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of…
We present a concise introduction to quantum entanglement. Concentrating on bipartite systems we review the separability criteria and measures of entanglement. We focus our attention on geometry of the sets of separable and maximally…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space-time is three dimensional.
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 present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
A local conception is proposed to reconcile quantum theory with general relativity, which allows one to avoid some difficulties --- as e.g. vacuum catastrophe --- of the global approach.