Conformal QED

Abstract

A conformally invariant quantum electrodynamics is constructed. The setting is realistic space-time (rather than Euclidean), and a complete Gupta–Bleuler quantization scheme is carried out. Conformal invariance of the quantum field theory (as opposed to either classical field theory or to a theory defined by its Feynman rules) requires a richer Gupta–Bleuler structure than has been considered previously. Yet the essential features of this structure are preserved. The requirement that the wave equation be of second order fixes a unique action that already contains the gauge-fixing terms that are required in any complete quantum field theory. The ‘‘Lorentz condition’’ turns out to be the transversality condition yαaα(y)=0 (in the manifestly covariant six-dimensional notation); this condition has to be treated in the same way as the Lorentz condition ∂μAμ(x)=0 (four-dimensional notation), as a boundary condition on the physical states.