QUANTIZATION OF THE PHOTON FIELD AND DIPOLE GHOSTS

Abstract：

We discuss the quantization of a massless vector field using the Lagrange mul-tiplier method. The exact solution of the field equations in three dimensional mo-mentum space is given and the existence of dipole ghosts explicitly demonstrated.One of the ghosts is not an eigenstate of the Hamiltonian and can be eliminated byboundary conditions. If the vector field is coupled to conserved currents, the otherghost has no observable effects. So this field theory describes the photon. This pro-blem has been studied by Nakanishi, but his analysis is obscure. The extension ofthis method to spin 3/2 massless field is discussed.