Gauge-field quantization

Abstract

The quantization of gauge fields by means of the Dirac–Bergmann Hamiltonian constraint formulation for generalized dynamical systems is criticized. This formulation is shown to be inconsistent with its implicit assumption that all variables are to be varied in Hamilton's principle and is overly restrictive when applied to simple models. It is shown that the Dirac–Bergmann formulation involves an unjustified assumption in addition to the natural assumption that the gauge field is dynamical. An alternative formulation that does not involve the unjustified assumption is proposed. In this, every variable whose time development is not determined by the equations of motion is treated as a reference, rather than a dynamical, variable and not varied in the action. The proposed formulation is applied to some simple examples, including electromagnetism.