Motivated by extending the parameter space of the Standard Model of Particle Physics, I will describe how to understand the effects of an imaginary mixing mass term in a non-Hermitian but PT-symmetric extension of scalar QED. The classical theory is already not trivial, and requires a new interpretation of the equations of motion, Noether's theorem and gauge invariance. The path integral can be defined with appropriate field variables, and a consistent picture emerges, opening the way for potential alternative descriptions of the Higgs sector.