Quantum particle

What follows is valid for fermions. Consider, for example, a particle with charge. For other particles, sensible to other kind of interactions, you simply take another group (not $U(1)$) for the internal symmetries. To formulate what is a charged particle (an electron) in QFT we follow these steps:

• We consider a principal bundle $P\to M$ with group $G=S{O}^{+}(1,n)\times U(1)$. We introduce a connection here to model the EM field (and maybe something more, I don't know).
• We consider an associated bundle $E\to M$, given by a group representation of $G$.
• For an particle with charge $q$ I think that "the part of the representation" corresponding to $U(1)$ is: $e^{i\theta }:v\mapsto e^{iq\theta }v$. See this.
• The "part of the representation" corresponding to $S{O}^{+}(1,n)$ affects the spinorial "character" of the particle.
• Sections of $E$ are classical fields yet, not particles. We can define Lagrangians to see their evolution.
• We "quantize" these fields (I have to understand this yet), and in the process some "basic excitation states" appears. This is a particle with charge $q$. See quantum field.

What about bosons? The connection is quantized, too, by promoting the gauge potential $A_{\mu }$ to operators...

Related: Standard Model.