D-Particle Dynamics and The Space-Time Uncertainty Relation

TL;DR

This paper demonstrates that the space-time uncertainty relation, combined with quantum mechanics, universally explains the qualitative features of D-particle dynamics in string theory.

Contribution

It establishes the universal validity of the space-time uncertainty relation in string theory, including D-branes, and explains D-particle behavior.

Findings

The space-time uncertainty relation applies to D-branes.

It explains key features of D-particle dynamics.

The relation complements quantum mechanics in string theory.

Abstract

We argue that the space-time uncertainty relation of the form $\Delta X \Delta T \gtrsim \alpha'$ for the observability of the distances with respect to time, $\Delta T$, and space, $\Delta X$, is universally valid in string theory including D-branes. This relation has been previously proposed by one (T.Y.) of the present authors as a simple qualitative representation of the perturbative short distance structure of fundamental string theory. We show that the relation, combined with the usual quantum mechanical uncertainty principle, explains the key qualitative features of D-particle dynamics.