Multi-field generalisations of the Klein-Gordon theory associated with p-branes

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.