Related papers: Lectures on Non Perturbative Field Theory and Quan…
Topological defects play a fundamental role in the investigation of symmetries in quantum field theories. For conformal field theories in two space-time dimensions, it is possible to construct these defects using lattice models allowing…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…
The fields nonlinear modes quantization scheme is discussed. New form of the perturbation theory achieved by unitary mapping the quantum dynamics in the space $W_G$ of (action, angle)-type collective variables. It is shown why the…
We review the main results of the effective description of the Quantum Hall fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by a conformal field theory (CFT) in two dimensions. It is stressed the unifying…
This is a set of introductory lecture notes on conformal field theory. Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. It begins with a…
Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited…
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
We develop an approach to investigate the non-perturbative dynamics of quantum field theories, in which specific vacuum field fluctuations are treated as the low-energy dynamical degrees of freedom, while all other vacuum field…
We study quantum field theory on a de Sitter spacetime dS$_{d+1}$ background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group $SO(d+1,1)$. As the first application of the Hilbert…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
Resonant tunnelling through an Anderson impurity is investigated by employing a new perturbation scheme at nonequilibrium. This new approach gives the correct weak and strong coupling limit in $U$ by introducing adjustable parameters in the…
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity…
The present thesis deals with some properties of classical and quantum scalar fields in an inhomogeneous and/or time-dependent background, focusing on models where the latter can be described as a curved space-time with an event horizon.…
Advantages of using a low-energy effective theory to study bound state properties are briefly discussed, and a nonperturbative implementation of such an effective theory is described within the context of nonrelativistic quantum mechanics.…
The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\alpha$, in Quantum Theory. We start with outlining a…
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set…
These lecture notes provide an elementary introduction to the study of massless integrable quantum field theory in 1+1 dimensions using ``massless scattering''. Some previously unpublished results are also presented, including a…
You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free…
Non-perturbative quantum general relativity provides a possible framework to analyze issues related to black hole thermodynamics from a fundamental perspective. A pedagogical account of the recent developments in this area is given. The…
We give a short introduction for elementary mathematical tools used in the context of Quantum Field Theory. These notes were motivated by a reading group in Lyon on Talagrand's book {\guillemotleft}What is Quantum Field Theory, A First…