Db. Fairlie et T. Ueno, Multi-field generalisations of the Klein-Gordon theory associated with p-branes, J HIGH EN P, 2001(4), 2001, pp. NIL_108-NIL_120
The purpose of this article is to initiate a study of a class of Lorentz in
variant, 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 participati
ng fields with respect to the base space co-ordinates. In the case of two f
ields, real valued solutions of the equations of motion are found and a phe
nomenon reminiscent of instanton behaviour is uncovered; an ansatz for a su
bsidiary equation which implies a solution of the full equations yields rea
l solutions in three-dimensional euclidean space. Each of these is associat
ed with a spherical harmonic function.