Exploring the Relationship Between Electric Charge and Gauge Symmetry

[LarryS]

Does the property of electric charge of an elementary or composite particle exist only within the context of gauge symmetry - of the complex phase of the wave function, i.e. does gauge symmetry define electric charge?

Thanks in advance.

 

[jambaugh]

I'd have to answer your question with a "no", in that electric charge is an empirically measurable quantity and one can conceivably construct a non-gauge based theory describing it.

 

[vanhees71]

Well, I'd say that the contrary is true. Electric charge by definition is only properly defined together with the electromagnetic field, and as a massless vector boson the electromagnetic field is necessarily a gauge field, as follows from the representation theory of the Poincare group. Thus the electric charge is defined via the current density the electromagnetic field couples to, and thus there is no way to define electric charge without also taking em. gauge symmetry into account. All observable phenomena about the property of matter carrying electric charge follow from electromagnetic interactions, including the detectors used to measure the particles involved in the interaction.