A Model for Classical Space-time Co-ordinates

TL;DR

This paper proposes a model where classical space-time coordinates are described as target space variables within a conformally invariant framework, offering a new perspective on reparametrisation invariant membranes.

Contribution

It introduces a novel interpretation of field equations with general covariance as target space equations and develops a membrane model by swapping base and target space roles.

Findings

Field equations admit infinite inequivalent Lagrangian descriptions.

A new membrane model with reparametrisation invariance is constructed.

Provides insights into the structure of space-time coordinates in a conformal setting.

Abstract

Field equations with general covariance are interpreted as equations for a target space describing physical space time co-ordinates, in terms of an underlying base space with conformal invariance. These equations admit an infinite number of inequivalent Lagrangian descriptions. A model for reparametrisation invariant membranes is obtained by reversing the roles of base and target space variables in these considerations.