Galileo invariant system and the motion of relativistic d-branes

TL;DR

This paper explores the connection between relativistic d-brane systems and Galileo invariant systems across various dimensions, providing explicit solutions and extending the results to higher dimensions.

Contribution

It introduces a method to relate relativistic d-brane dynamics to Galileo invariant systems and solves these systems explicitly in multiple dimensions.

Findings

Solutions for d-brane systems in (2,1), (3,1), and (4,1) dimensions

Demonstrates the correspondence with Galileo invariant systems in lower dimensions

Extends the analysis to higher-dimensional cases

Abstract

We follow recent work and study the relativistic d-brane system in (d+1,1) dimensions and its connection with a Galileo invariant system in (d,1) dimensions. In particular, we solve d-brane systems in (2,1), (3,1) and (4,1) dimensions and show that their solutions solve the corresponding Galileo invariant systems in (1,1), (2,1), and (3,1) dimensions. The results are extended to higher dimensions.