Related papers: Topos-Theoretic Approaches to Quantum Theory
There exist dozens of interpretations of quantum theory, but they do not seem to contribute much to understanding the theory. This paper attempts to clarify some issues that are discussed in those interpretations. The main keywords are:…
Many attempts have been made to provide Quantum Field Theory with conceptually clear and mathematically rigorous foundations; remarkable examples are the Bohmian and the algebraic perspectives respectively. In this essay we introduce the…
Quantum substitutions of Pisot type (and their quantum topological entropy) are introduced. Their utility as algorithms for optimal spacing is analyzed.
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
Contents 1 Mappings and distortion 2 The mathematics of good behavior much of the time, and the BMO frame of mind 3 Finite polyhedra and combinatorial parameterization problems 4 Quantitative topology, and calculus on singular spaces 5…
This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…
In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational work of Benini et al. by providing a richer framework to…
We describe quantum theories for massless (p,q)-forms living on Kaehler spaces. In particular we consider four different types of quantum theories: two types involve gauge symmetries and two types are simpler theories without gauge…
Omnes' interpretation of quantum mechanics is summarized, and compared with other consistent-history approaches by Gell-Mann and Hartle, and by Griffiths.
An idealised 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…
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…
The development of quantum theory on a torus has a long history, and can be traced back to the 1920s, with the attempts by Nordstr\"om, Kaluza and Klein to define a fourth spatial dimension with a finite size, being curved in the form of a…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
We formulate quantum theory taking as a starting point the cone of states.
A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the…
This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M.…
The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum…