How can you model charge?

[Ben vdP]

TL;DR

An elementary particle has properties like spin and charge.
With spin there can be some kind of notion of rotation, but how can charge be characterized?

Does there exists some underlying views or models on charge?

An elementary particle has properties like spin and charge.
With spin there can still be some kind of notion of rotation, but how can charge be characterized?

Does there exists some underlying views or models on charge?


Pragmatically, charge can be seen as a strength of coupling with photon fields.
That answers more the question of "what it does" rather than "what it is".
It doesn't say why it couples with photons, based on some underlying model or idea.
(Discussions on that can run into lots of circles though).


In EM, charge looks more like a given, i.e. dealing with the consequences of charge being present
or moving as currents (Gauss, Maxwell laws) resulting into fields and forces and phenomena or dynamics.
EM has nothing to say about what charge actually is as far as I can see.
Has that picture changed in QM or QFT?


Consider dark matter, it does not interact with light directly so can it have no charge, or is may there be a forbidden coupling.
For example, if it has an inverted toroidal field or anapole with the magnetic lines going around the middle instead of going from pole to pole,
what would that say about the nature of charge or the internal (moving) charge distribution?
There is a technical term for such a particle, but it escaped me for the moment.

Any ideas?

 

[QuarkyMeson]

An elementary particle has properties like spin and charge.
With spin there can still be some kind of notion of rotation, but how can charge be characterized?

Spin is a quantum mechanical property. It's intrinsic angular momentum which isn't literally a classical rotation at all. Take an electron, it has spin but lacks any classical rotational degrees of freedom.

Does there exists some underlying views or models on charge?

Charge is the same, it's a quantum mechanical property.

At the end of the day spin is the quantum number associated with the representation of the Lorentz group, while charge is the quantum number associated with internal gauge symmetry.

Consider dark matter, it does not interact with light directly so can it have no charge, or is may there be a forbidden coupling.
For example, if it has an inverted toroidal field or anapole with the magnetic lines going around the middle instead of going from pole to pole,
what would that say about the nature of charge or the internal (moving) charge distribution?
There is a technical term for such a particle, but it escaped me for the moment.

Majorana Fermions.
https://arxiv.org/abs/2207.01014

 

[Orodruin]

The previous reply is excellent, so I will just add that the role of physics as an empirical science is to describe how things work, not to provide some underlying truth.

You can always search for more detailed models, but physics will never describe what

actually is

 

[Ben vdP]

That charge is the quantum number associated with internal U1 gauge symmetry is something that I can live with.
It may be futile to look for some field characterisation or geometric explanation of charge.

That physics is only an empirical science can be nuanced somewhat, it leads also to abstractions and insights and models. But that would be a different discussion.

Thanks for the link on Majorana Fermions.