Gauge Invariance in Quantum Electrodynamics

Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant fields. We show that all the formulations, such as the Coulomb, the axial, and the Lorentz gauges, can be constructed and that the explicit LSZ mapping connecting Heisenberg operators to those of the asymptotic fields is possible. We also make some comments on gauge transformations in quantized field theory.