Under these conditions, the theory will involve quantum electrodynamics with a massless photon, a charged scalar field ϕ and a mass μ4. However, if μ2 > 0, the field will obtain a vacuum expectation value as below, (17) and in such a case the global U(1) symmetry will be spontaneously broken. A parameterized ϕ has the following form, (18) where h and χ are the Higgs boson and the Goldstone boson, respectively, represent real scalar fields without vacuum expectation values. If we substitute this scalar field for the original Lagrangian, we obtain the following4, (19) This new derived Lagrangian describes a photon with mass mA = ev, a Higgs boson h with the following mass, (20) as well as a Goldstone massless χ. Furthermore, to remove the χ-Aμ mixture, it is possible to remove the Lagrangian via the following gauge