Related papers: Quantum Theory and Galois Fields
These lecture notes, prepared for the 2022 QUC summer school at KIAS, provide an introduction to Higgs Effective Field Theory and the use of field geometry in Quantum Field Theory. While not sounding the depths of any of these topics, we…
We discuss several proposals for astrophysical and cosmological tests of quantum theory. The tests are motivated by deterministic hidden-variables theories, and in particular by the view that quantum physics is merely an effective theory of…
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
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…
This is a further explanation of a new and simple renormalization approach recently proposed by the author (hep-th/9708104, Ref. [1], that is somewhat sketchy) for any ordinary QFT (whether renormalizable or not) in any spacetime dimension.…
Topos theory has been suggested by D\"oring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular, the topos approach suggests a radical new way of thinking about what a theory of…
The traditional, standard approach to quantum theory is to assume that the theory ``really'' contains only unitary physical dynamics--i.e., that the only physically quantifiable evolution is that given by the time-dependent Schrodinger…
This volume contains a selection of papers presented at the 9th in a series of international conferences on Quantum Simulation and Quantum Walks (QSQW). During this event, we worked on the development of theories based upon quantum walks…
Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…
Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…
Controlling the continuum limit and extracting effective gravitational physics are shared challenges for quantum gravity approaches based on quantum discrete structures. The description of quantum gravity in terms of tensorial group field…
Quantum set theory (QST) and topos quantum theory (TQT) are two long running projects in the mathematical foundations of quantum mechanics that share a great deal of conceptual and technical affinity. Most pertinently, both approaches…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
Quantum gravity is the missing piece in our understanding of the fundamental interactions today. Given recent observational breakthroughs in gravity, providing a quantum theory for what lies beyond general relativity is more urgent than…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual…
In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown…