Notes on matrix models (matrix musings)
Dionysios Anninos, Beatrix Mühlmann
Abstract
Abstract 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 matrix-like fashion. We discuss the relation of matrix models to two-dimensional quantum gravity coupled to conformal matter. We provide a brief overview of a variety of more general quantum mechanical matrix models and their putative worldsheet interpretation, as well as other recent developments on large N systems. We end with a discussion of open questions and future directions.
Topics & Concepts
Variety (cybernetics)Hermitian matrixQuantumConformal mapDegrees of freedom (physics and chemistry)WorldsheetMatrix (chemical analysis)Theoretical physicsRelation (database)PhysicsAlgebra over a fieldQuantum gravityMatrix modelComputer scienceMathematicsMinimal modelsPure mathematicsStatistical physicsS-matrixClassical mechanicsWork (physics)Algebraic structures and combinatorial modelsQuantum Mechanics and Non-Hermitian PhysicsBlack Holes and Theoretical Physics