Related papers: Perturbation Theory and Techniques
This is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.
Quantum gravity is an important and to great extent unsolved problem. There are many different approaches to the quantization of the metric field, both perturbative and non-perturbative. The current situation in the perturbative quantum…
The evolution of the distribution-theoretic methods in perturbative quantum field theory is reviewed starting from Bogolyubov's pioneering 1952 work with emphasis on the theory and calculations of perturbation theory integrals.
In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level…
In strongly coupled field theories, perturbation theory cannot be employed to study the low-energy spectrum. Thus, non-perturbative techniques are required. We employ the variational method, a rigorous, non-perturbative approach which…
This is the foreword to the special volume on localization techniques in quantum field theory. We summarize the individual chapters and their relation.
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the…
We give a pedagogical introduction to quantum anomalies, how they are calculated using various methods, and why they are important in condensed matter theory. We discuss axial, chiral, and gravitational anomalies as well as global…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…
I propose a prescription for separating the high- and low-energy contributions in effective field theories. This prescription allows a relativistic treatment of matter fields in chiral perturbation theory while the power counting remains…
We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds…
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.
A brief introduction to the low-energy effective field theory of the standard model, chiral perturbation theory, is presented.
These notes contain the written version of lectures given at the 2009 Les Houches Summer School "Modern perspectives in lattice QCD: Quantum field theory and high performance computing." The goal is to provide a pedagogical introduction to…
For a wide class of nonlinear equations a perturbative solution is constructed. This class includes equations of motion of field theories. The solution possesses a graphical representation in terms of diagrams. To illustrate the formalism…