Reduction formulas for quantum electrodynamics

The problem of deriving the Lehmann-Symanzik-Zimmermann reduction formulas for manifestly covariant quantum electrodynamics is reexamined. The problem of defining states which satisfy the Gupta-Bleuler condition in the infrared limit is resolved by applying a nonlocal instantaneous pseudounitary transformation to the direct-product Fock space before applying the infrared transformation. These states are reduced to find that the interpolating Heisenberg spinor fields pick up an operator-valued phase which makes them manifestly gauge invariant. The time-ordered products associated with the scattering amplitudes are shown to have perturbative representations consistent with the form of asymptotic limits selected for the interpolating fields. The phase on the spinor fields causes the $S$ matrix to have the usual Coulomb-gauge Feynman rules, while the infrared problem is resolved by developing the infrared form for the asymptotic Coulomb-gauge fields. Strict satisfaction of the Gupta-Bleuler condition is seen to be unnecessary in a charge-conserving theory.