  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.
