Equivalence of null-plane and conventional quantum electrodynamics

Publisher Website
Google Scholar
Abstract
We prove the physical equivalence of null-plane quantum electrodynamics in the null-plane gauge to conventional quantum electrodynamics in the Coulomb gauge. This is done formally within the framework of Feynman-Dyson-Schwinger theory. The equivalence of the dynamical equations and of the commutation relations in the two formulations is proven in the Heisenberg picture. In the interaction picture this requires that the free fields be defined over a test-function space corresponding physically to the absence of photons propagating along one space axis (which can be chosen arbitrarily). The proof has the virtue of being based on a positive-definite Hilbert space. This is possible because the null-plane gauge, as well as the Coulomb gauge, does not require supplementary conditions on state vectors nor fields with "wrong" commutation relations. A great deal of complexity of formalism is thereby avoided.