Related papers: Localization techniques in quantum field theories
A brief description of the relations between the factorization method in quantum mechanics, self-similar potentials, integrable systems and the theory of special functions is given. New coherent states of the harmonic oscillator related to…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.
The use of quantum field theory to understand astrophysical phenomena is not new. However, for the most part, the methods used are those that have been developed decades ago. The intervening years have seen some remarkable developments in…
We give a leisurely, albeit woefully incomplete, overview of quantum field theory, its relevance to condensed matter systems, and spin systems, which proceeds via a series of illustrative examples. The goal is to provide readers from the…
Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and…
We report on joint work, past and in progress, with K.Fredenhagen and with J.E,Roberts, on the quantum structure of spacetime in the small which is dictated by the principles of Quantum Mechanics and of General Relativity; we comment on how…
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties…
An overview of the accomplishments of constructive quantum field theory is provided.
We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes…
We give an introduction to the theory of multi-partite entanglement. We begin by describing the "coordinate system" of the field: Are we dealing with pure or mixed states, with single or multiple copies, what notion of "locality" is being…
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…
In this contribution we use the model of discrete spaces that we have put forward in former articles to give an interpretation to the phenomena of quantum entanglement and quantum states reduction that rests upon a new way of considering…
We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and results have the clear flavor of a localization theorem.
In this lecture note we demonstrated the capability of the local distribution approach to the problem of quantum percolation.
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
In this article we give an introduction to the Fock quantization of the Maxwell field. At the classical level, we treat the theory in both the covariant and canonical phase space formalisms. The approach is general since we consider…
We analyze the property of locality with respect to the framework for quantum mechanics based on the path integral formalism. As is well known, this framework makes the same experimental predictions as does the one based on a separable…
We derive equivariant localization formulas of Atiyah--Bott and cohomological field theory types in the Batalin-Vilkovisky formalism and discuss their applications in Poisson geometry and quantum field theory.
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…