Canonical Field Theory—A Prototype Example

The equations of a field may be put into a standard “Lagrangian” form from which several conservation laws follow directly. As an illustrative example, a string free to vibrate in two directions is investigated; this example clearly illustrates the outstanding features of the canonical theory, while avoiding the notational and physical complications encountered in most systems of practical interest. The conservation laws are interpreted for the string. The theory is further developed to express the field's behavior in terms of canonical coordinates and momenta. Quantum conditions are introduced, as in meson theory and quantum electrodynamics. It is shown that the mathematics of the “quantized string” is that of several charged particles occupying a set of energy states.