Multi-Field Generalisations of the Klein-Gordon Theory associated with p-Branes

TL;DR

This paper introduces a new class of Lorentz-invariant multi-field Lagrangian theories extending Klein-Gordon models, revealing solutions with instanton-like behavior and spherical symmetry in Euclidean space.

Contribution

It proposes a novel multi-field Lagrangian extending Klein-Gordon theory, analyzing solutions and instanton-like phenomena in a new tractable framework.

Findings

Real solutions found for two-field equations of motion

Discovery of instanton-like phenomena in the model

Solutions associated with spherical harmonics in Euclidean space

Abstract

The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These Lagrangians are quadratic in the Jacobians of the participating fields with respect to the base space co-ordinates. In the case of two fields, real valued solutions of the equations of motion are found and a phenomenon reminiscent of instanton behaviour is uncovered; an ansatz for a subsidiary equation which implies a solution of the full equations yields real solutions in three-dimensional Euclidean space. Each of these is associated with a spherical harmonic function.