A field is a dynamically changing potential V(x, t), which evolves in time according to an equation of motion. The equation of motion is a constraint on the allowed behaviour of the field. It expresses the dynamical content of the theory. The solution of that constraint, called the physical field, is the pivotal variable from which we glean all of the physical properties of the system. In addition to dynamical equations, a field theory has a conceptual basis composed of physical assumptions, interpretations and boundary conditions.

The familiar equations of motion, in classical field dynamics, include the Schrödinger equation, Maxwell's equations, Dirac's relativistic equation and several others. In the context of field theory, we call such equations classical as long as we are not doing quantum field theory (see chapter 15), since the method of solution is directly analogous to that of classical electrodynamics. In spite of this designation, we know that the solutions of Schrödinger's field equation are wavefunctions, i.e. the stuff of quantum mechanics. Whole books have been written about these solutions and their interpretation, but they are not called field theory; they use a different name.

Field theory embraces both quantum mechanics and classical electrodynamics, and goes on to describe the most fundamental picture of matter and energy known to physics. Our aim here is to seek a unified level of description for matter and radiation, by focusing on a field theoretical formulation. This approach allows a uniquely valuable perspective, which forms the basis for the full quantum theory.