Advances in classical field theory

Classical field theory is used by physicists to describe a wide variety of physical phenomena. Those include electromagnetism, fluid dynamics, gravitation and quantum mechanics. The central entity of field theory is the field which is usually a multi component function of space and time. Those multi component functions are usually grouped together as vector fields as in the case of electromagnetic theory and fluid dynamics, in other cases they are grouped as tensors as in theory of gravitation and yet in other cases they are grouped as complex functions as in the case of quantum mechanics. In order to know the value of the field one needs to solve a set of coupled partial differential equations with given boundary and initial conditions. Both the equations and the boundary and initial conditions are in most cases available from a variational principle through an adequate Lagrangian, although in some cases this is less straight forward as in the case of fluid dynamics. An appropriate field theory satisfies two main requirements: First it should describe correctly the relevant physical phenomena and second the theory should describe the phenomena with a minimal number of functions, equations and assumptions. Advances in classical theory have thus two principal meanings. One meaning is improvement of a known theory in the sense that the new theory proposed now describes correctly a wider class of physical phenomena. A second meaning is that a given physical phenomena is described by less functions, equations or assumptions than was needed before.