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A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
We formulate a stochastic generalisation of the Schwinger effect, extending pair production to statistically fluctuating gauge-field backgrounds. Our approach captures realistic field configurations that are transient, inhomogeneous, and…
The purpose of the present paper is the communication of some results and observations which shed new light on the algebraic structure of the algebra of string observables both in the classical and in the quantum theory.
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible…
With the SNOWMASS 2021 process in the US and the on--going European Strategy Report 2025, the field of elementary particle physics is undergoing detailed community evaluation, and the experimental particle physics program, which requires…
We review Grover's algorithm by means of a detailed geometrical interpretation and a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are also reviewed. This work is intended for non-specialists which have…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
The four-dimensional superstring solutions define at low energy effective supergravity theories. A class of them extends successfully the validity of the standard model up to the string scale (${\cal O}(10^{17})~TeV$). We stress the…
A method of constructing a canonical gauge invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of closed bosonic string interacting with massive…
String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…
These are introductory lectures for a general audience that give an overview of the subject of matrix models and their application to random surfaces, 2d gravity, and string theory. They are intentionally 1.5 years out of date. 0. Canned…
In these introductory notes I explain some basic ideas in string field theory. These include: the concept of a string field, the issue of background independence, the reason why minimal area metrics solve the problem of generating all…
This thesis is based on two papers by the author and consists of two parts. We review the recent developments in the theory of multiple M2-branes and 3-algebras leading to multiple D2-brane theories. The inclusion of flux terms for the…
Complex structures are determined for surfaces with $S^2$ and $T^2$ topologies generated by the dynamical triangulation method. For a surface with $S^2$ topology the spacial distribution of the conformal mode is obtained, while for the case…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
String breaking is a fundamental concept in gauge theories, describing the decay of a flux string connecting two charges through the production of particle-antiparticle pairs. This phenomenon is particularly important in particle physics,…