Rotation of D-brane and Non-commutative Geometry

TL;DR

This paper explores how rotating D-branes relate to non-commutative geometry, analyzing boundary conditions, mode expansions, and scattering amplitudes to understand coordinate commutators and uncertainty relations.

Contribution

It introduces a more consistent mode expansion for rotated D-branes and links boundary conditions with non-commutative geometry concepts.

Findings

Mode expansions are more reasonable than previous literature

Boundary conditions relate to non-commutative geometry

Partition functions and scattering amplitudes are analyzed

Abstract

Our motivation is to find the relationship between the commutator of coordinates and uncertainty relation involving only the coordinates. The boundary condition with constant background field is connected with the rotation of D-brane at general angle. And the mode expansions of D-brane we found is more reasonable than those appeared in literature. The partition functions and scattering amplitudes are also discussed.