Coupling Electromagnetism to Global Charge

Abstract: It is shown that an alternative to the standard scalar QED is possible. In this new version there is only global gauge invariance as far as the charged scalar fields are concerned although local gauge invariance is kept for the electromagnetic field. The electromagnetic coupling has the form $j_\mu (A^{\mu} +\partial^{\mu}B)$ where $B$ is an auxiliary field and the current $j_\mu$ is $A_{\mu}$ independent so that no "sea gull terms" are introduced. In a model of this kind spontaneous breaking of symmetry does not lead to photon mass generation, instead the Goldstone boson becomes a massless source for the electromagnetic field. Infrared questions concerning the theory when spontaneous symmetry breaking takes place and generalizations to global vector QED are discussed. In this framework Q-Balls and other non topological solitons that owe their existence to a global U(1) symmetry can be coupled to electromagnetism and could represent multiply charged particles now in search in the LHC. Furthermore, we give an example where an "Emergent" Global Scalar QED can appear from an axion photon system in an external magnetic field. Finally, formulations of Global scalar QED that allow perturbative expansions without sea gulls are developed.