Related papers: Axiomatic Quantum Theory
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational…
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 field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems,…
It is shown that adopting the \emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements: * Coherent quantum physics…
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum…
This paper explains some fundamental ideas of {\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and…
This is a series of lecture notes explaining topos theory and its application in physics.
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Practically measurable quantities resulting from quantum field theory are not described by hermitian operators, contradicting one of the cornerstone axioms of orthodox quantum theory. This could be a sign that some of the axioms of orthodox…
We present an axiomatization of non-relativistic Quantum Mechanics for a system with an arbitrary number of components. The interpretation of our system of axioms is realistic and objective. The EPR paradox and its relation with realism is…
Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…
In this lecture we discuss the basic ingredients for gauge invariant quantum field theories. We give an introduction to the elements of quantum field theory, to the construction of the basic Lagrangian for a general gauge theory, and…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…