Massive Vector Field and Electromagnetic Field in the Landau Gauge

Abstract

It is shown that by introducing an auxiliary scalar field having negative norm, one can formulate a consistent, manifestly covariant, and manifestly renormalizable theory of a neutral vector field. The $S$ matrix is unitary if the vector field couples with a conserved current. An important feature of this theory is that it smoothly tends to quantum electrodynamics in the Landau gauge when the bare mass of the vector field goes to zero. On the basis of this fact, one resolves the drawback of Johnson's proof of the statement that the physical mass of the vector field must vanish when its bare mass vanishes. Furthermore, it is explicitly demonstrated how the vacuum expectation value of the commutator of Heisenberg operators behaves as the mass tends to zero. Finally, an extension of this theory to the massive Yang-Mills field is briefly discussed.