Related papers: Lectures on Non Perturbative Field Theory and Quan…
We explain in this paper how a meaningful irrelevant perturbation theory around the infra-red (strong coupling) fixed point can be carried out for integrable quantum impurity problems. This is illustrated in details for the spin 1/2 Kondo…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
The content of this paper is incorporated into hep-th/9805093
This is the preliminary manuscript of a book on symplectic field theory based on a lecture course for PhD students given in 2015-16. It covers the essentials of the analytical theory of punctured pseudoholomorphic curves, taking the…
These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students,…
This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite…
We study the effects of impurity scattering on the low energy edge state dynamic s for a broad class of quantum Hall fluids at filling factor $\nu =n/(np+1)$, for integer $n$ and even integer $p$. When $p$ is positive all $n$ of the edge…
In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
We present a construction of non-equilibrium steady states within conformal field theory. These states sustain energy flows between two quantum systems, initially prepared at different temperatures, whose dynamical properties are…
We dwell upon certain points concerning the meaning of quantum field theory, among these the problems with the perturbative approach, and the question raised by tHooft of the existence of the theory in a well defined mathematical sense, as…
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and…
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in…
Several issues in the modal approach to quantum field theory are discussed. Within the formalism of spherical field theory, differential renormalization is presented and shown to result in a finite number of renormalization parameters.…
What is quantum geometry? This question is becoming a popular leitmotiv in theoretical physics and in mathematics. Conformal field theory may catch a glimpse of the right answer. We review global aspects of the geometry of conformal fields,…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
Lecture notes for the course "Batalin-Vilkovisky formalism and applications in topological quantum field theory" given at the University of Notre Dame in the Fall 2016 for a mathematical audience. In these lectures we give a slow…
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…