Dynamical Aspects of Large N Reduced Models
نویسندگان
چکیده
We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We first put an upper bound on the extent of space time by perturbative arguments. We perform a Monte Carlo simulation and show that the upper bound is actually saturated. The relation of our result to the SSB of the U(1)D symmetry in the Eguchi-Kawai model is clarified. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of space time, which means that a classical space-time picture is maximally broken. We develop a 1/D expansion, which enables us to calculate correlation functions of the model analytically. The absence of an SSB of the Lorentz invariance is shown by the Monte Carlo simulation as well as by the 1/D expansion. ∗ e-mail address : [email protected], JSPS Research Fellow. † e-mail address : [email protected], [email protected] ‡ Present address : Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark § e-mail address : [email protected]
منابع مشابه
A new reduced mathematical model to simulate the action potential in end plate of skeletal muscle fibers
Usually mathematicians use Hodgkin-Huxley model or FitzHug-Nagumo model to simulate action potentials of skeletal muscle fibers. These models are electrically excitable, but skeletal muscle fibers are stimulated chemically. To investigate skeletal muscle fibers we use a model with six ordinary differential equations. This dynamical system is sensitive to initial value of some variables so it is...
متن کاملScaling relations in dynamical evolution of star clusters
We have carried out a series of small scale collisional N-body calculations of single-mass star clusters to investigate the dependence of the lifetime of star clusters on their initial parameters. Our models move through an external galaxy potential with a logarithmic density profile and they are limited by a cut-off radius. In order to find scaling relations between the lifetime of star cluste...
متن کاملNORMAL FORM SOLUTION OF REDUCED ORDER OSCILLATING SYSTEMS
This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...
متن کاملDynamical Properties of Large N Reduced Model of Yang-Mills Theory
We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to the dynamical aspects related to the eigenvalues of the N ×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of the space time, whi...
متن کاملDynamical Properties of Large N Reduced Model of Yang - Mills Theory
We study the large N reduced model of D-dimensional Yang-Mills theory with special attention to the dynamical aspects related to the eigenvalues of the N ×N matrices, which correspond to the space-time coordinates in the IIB matrix model. We define a quantity which represents the uncertainty of the space-time coordinates and show that it is of the same order as the extent of the space time, whi...
متن کاملExtension Ability of Reduced Order Model of Unsteady Incompressible Flows Using a Combination of POD and Fourier Modes
In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynam...
متن کامل