相关论文: 2D Quantum Gravity, Matrix Models and Graph Combin…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
We review recent work in the lattice approach to random surfaces and quantum gravity. Our task is made somewhat easier by some very interesting results, particularly in four dimensions, that have appeared recently and which are reported…
This is an expanded version of the lectures given at the Trieste Summer School 1992 on Low-dimensional Quantum Field Theories for Condensed Matter Physicists.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
Lectures given at the Trieste Summer School, 1992. These notes are an update of my review article "Classical and Quantum W-Gravity", preprint QMW-92-1, published in in "Strings and Symmetries 1991", with some extra material on W-geometry,…
These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects,…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
The AdS/CFT correspondence provides quantum theories of gravity in which spacetime and gravitational physics emerge from ordinary non-gravitational quantum systems with many degrees of freedom. Recent work in this context has uncovered…
These notes are an account of a series of lectures given at the Les Houches Summer School "Active Matter and Non-equilibrium Statistical Physics" during August and September 2018. The lectures can be viewed online at…
The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos.…
These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the…
In these lecture notes for the Les Houches School on Applications of Random Matrices in Physics we give an introduction to the connections between matrix models and topological strings. We first review some basic results of matrix model…
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic…
The author recalls general tendencies of the "mathematization" of the sciences and derives challenges and tentative obstructions for a successful merger of mathematics and physics on fancied steps towards "Quantum Gravity". This is an…
Lectures given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009
This lecture note surveys the gamma matrices in general dimensions with arbitrary signatures, the study of which is essential to understand the supersymmetry in the corresponding spacetime. The contents supplement the lecture presented by…
Lectures given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009
Content: 1. Introduction 2. Regge calculus and dynamical triangulations Simplicial manifolds and piecewise linear spaces - dual complex and volume elements - curvature and Regge action - topological invariants - quantum Regge calculus -…
This is an expanded version of talks given by the author at the Trieste Spring School on Supergravity and Superstrings in April of 1997 and at the accompanying workshop. The manuscript is intended to be a mini-review of Matrix Theory. The…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…