Related papers: Some Basic Tools of QFT
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
This course on Feynman integrals starts from the basics, requiring only knowledge from special relativity and undergraduate mathematics. Topics from quantum field theory and advanced mathematics are introduced as they are needed. The course…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schr\"odinger field theory, obtaining the Schr\"odinger…
Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering natural unitary representations of a group $K\subset U(2,2)$, where $K$ is locally…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other…
We show, in great detail, how the perturbative tools of quantum field theory allow one to rigorously obtain: a ``categorified'' Faa di Bruno type formula for multiple composition, an explicit formula for reversion and a proof of…
We present a practical course targeting graduate students with prior knowledge of the basics of quantum computing. The practical aims to deepen students' understanding of fundamental concepts in quantum computing by implementing quantum…
Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT, therefore, constitutes a natural application-centric…
Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research…
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
Random matrix models have been extensively studied in mathematical physics and have proven useful in combinatorics. In this review paper we introduce a generalization of these models to a class of tensor models. As the topology and…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
We review the main features of the relativistic Snyder model and its generalizations. We discuss the quantum field theory on this background using the standard formalism of noncommutaive QFT and discuss the possibility of obtaining a finite…
The milq approach to quantum physics for high schools focuses on the conceptual questions of quantum physics. Students should be given the opportunity to engage with the world view of modern physics. The aim is to achieve a conceptually…