Related papers: Topos-Theoretic Approaches to Quantum Theory
All current approaches to quantum gravity employ essentially standard quantum theory including, in particular, continuum quantities such as the real or complex numbers. However, I wish to argue that this may be fundamentally wrong in so far…
Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented.
The topos approach to the formulation of physical theories includes a new form of quantum logic. We present this topos quantum logic, including some new results, and compare it to standard quantum logic, all with an eye to conceptual…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
To each quantum system, described by a von Neumann algebra of physical quantities, we associate a complete bi-Heyting algebra. The elements of this algebra represent contextualised propositions about the values of the physical quantities of…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth value to a proposition that the…
This article reviews the 2008 quantum algorithm for linear systems of equations due to Harrow, Hassidim and Lloyd, as well as some of the followup and related work. It was submitted to the Springer Encyclopedia of Algorithms.
We present a conceptually clear introduction to quantum theory, deriving the theory from scratch from the point of view of quantum information. Different subsets of these lectures were taught to a wide variety of audiences, including…
An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
In a recent paper [12], we discussed the serious inconsistency present within the operational and mathematical definition(s) of the notion of pure state. Continuing this analysis, in this work we attempt to address the role of 'purity' and…
According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum…
Some explanations and implications of the underlying theory approach for quantum theories (QM or QFT) are discussed and suggested. This simple idea seems to have significantly nontrivial effects for our understanding of the quantum…
Topos quantum mechanics, developed by Isham et. al., creates a topos of presheaves over the poset V(N) of abelian von Neumann subalgebras of the von Neumann algebra N of bounded operators associated to a physical system, and established…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
An elementary review of quantum cosmology. (Talk given at Texas/Pascos 1992 at Berkeley)
In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two…
This is an essay review of the book by D. Home: "Conceptual Foundations of Quantum Physics: An Overview from Modern Perspectives" (New York: Plenum Press, 1997), xvii+386 pp., ISBN 0-306-45660-5.
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object, analogous to the state space of a…
The paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction formula for diagrams is proved, the presence…