Related papers: Some Basic Tools of QFT
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics…
In this contribution we give an introduction to the foundations and methods of lattice gauge theory. Starting with a brief discussion of the quantum mechanical path integral, we develop the main ingredients of lattice field theory:…
We describe the development and implementation of research-based learning tools such as the Quantum Interactive Learning Tutorials (QuILTs) and peer instruction tools to reduce students' common difficulties with issues related to…
The form factor of hadronic systems in various forms of relativistic quantum mechanics is considered. Motivated by the agreement of the nucleon ``point-form'' results with experiment, results for a toy model corresponding to the simplest…
This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic…
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…
Using the spectral properties of orthogonal polynomials, we introduce a finite version of quantum field theory for elementary particles. Closed-loop integrals in the Feynman diagrams for computing transition amplitudes are finite.…
In this short review we first recall combinatorial or ($0-$dimensional) quantum field theory (QFT). We then give the main idea of a standard QFT method, called the intermediate field method, and we review how to apply this method to a…
These notes are a didactic overview of the non perturbative and background independent approach to a quantum theory of gravity known as loop quantum gravity. The definition of real connection variables for general relativity, used as a…
Review of the most basic issues appearing in the most conservative approaches to quantum theory of gravity is given. The most part of the review is devoted to issues of perturbative quantization based on functional integral technique.…
Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL(2,C). Even though many monographs exist devoted to this theory, the different tools needed (e.g. representation theory, harmonic…
We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem,…
These lectures present a brief introduction to measurement theory for QFT in possibly curved spacetimes introduced by the author and R. Verch [Comm. Math. Phys. 378 (2020) 851-889]. Topics include: a brief introduction to algebraic QFT,…
This study presents a review of the current state of research on teaching quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory…
These notes were inspired by the course ''Quantum Field Theory from a Functional Integral Point of View'' given at the University of Zurich in Spring 2017 by Santosh Kandel. We describe Feynman's path integral approach to quantum mechanics…
Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short note we refine the meaning of qubits within the framework…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit…
These lecture notes formed the basis of a mini-course on algebraic quantum field theory presented at the Bootstrap 2024 conference in Madrid. The goal of the notes is to explain the merits of algebraic quantum field theory to a broad…
Since the introduction of quantum mechanics, it has been taught mostly as a theoretical subject. It is also viewed as a theory that provides a best understanding of the nature, but which does not have much practical applications in our day…