On Non-Abelian Structure From Matrix Coordinates

We consider the matrix quantum mechanics of N D0-branes in the background of the 1-form RR field. It is observed that the transformations of matrix coordinates of D0-branes induce on the Abelian RR field symmetry transformations that are like those of non-Abelian gauge fields. The Lorentz-like equations of motion for matrix coordinates are derived. The field strengths appearing in the Lorentz-like equations transform in the adjoint representation of U(N) under symmetry transformations. A possible relation between D0-brane dynamics in RR background, and the semi-classical dynamics of charged particles in Yang-Mills background is mentioned.Comment: 12 pages, no figures, LaTeX. v2: typos fixed, to appear in Phys. Lett.

First-Order Phase Transition by XY Model of Particle Dynamics

A gas-liquid type of phase transition is found based on the particle dynamics on radius-$R$ circle in which the coordinate appears as the angle-variable of 1D XY-model. Due to the specific appearance of compact-space radius (volume) in the present interpretation of XY-model, the ground-state develops a minimum at some critical radius, leading to the multi-valued Gibbs energy similar to systems with first-order phase transition.Comment: v1: LaTeX, 7 pages, 3 figs; v2: 9 pages, 5 figs, detailed comparison with magnetic system interpretation of XY-model is presented. Accepted for EP

Point-Like Structure in Strings and Non-Commutative Geometry

Dynamics of a free point particle on a multi world-line is presented and shown to reduce to that of a bosonic string theory at the appropriate limit. Other higher dimensional extended objects are argued to appear at other regions of the space of configurations of the theory.Comment: Latex file, 9 pages, minor alterations, 29.5 kb; to appear in Phys. Lett.