Some properties of the linearized model of the (super)$p$-brane

TL;DR

This paper explores the properties of the linearized relativistic p-brane model, including solutions, quantization, and extensions to supermembranes, providing insights into its mathematical structure and physical implications.

Contribution

It presents the solutions of the linearized p-brane equations of motion and discusses generalizations to supermembranes, advancing understanding of their properties and quantization.

Findings

Solutions for p-brane equations of motion with arbitrary topology

Quantization results including critical dimension

Extensions to supermembrane models

Abstract

Some general properties of the relativistic $p$-dimensional surface imbedded into $D$-dimensional spacetime and its reduction to the sim\-plest case of the quadratic Lagrangian (the linearized model) are considered. The solutions of the equations of motion of the linearized model for the $p$-brane with arbitrary topology and massless eigenstates, as well as with critical dimension after quantization are presented. Some generalizations for the supermembrane are discussed.