I’m speaking of bare particles. “Heroes” is maybe too pathetic, but “bricks” would be OK since everything is made of them despite their being non-observable. Why are they non-observable? Because they are non-interacting particles or particles “before interaction”. Inaccessible, for short.
It is relativistic and gauge-invariant because the bare particles are such. Parameters and are bare particle mass and charge and the term is how bare particles interact. Of course, bare particles have spin and other quantum numbers.
You may wonder how do we physicists know all that if the bare particles are non-observable (and why do they interact if they are non-interacting particles)?
Good questions. Very intelligent! The answer is – due to our physical insights. You know, insight is the ability to see the invisible, to penetrate mentally into the unknown, to figure out everything correctly from small, rare, and distorted pieces of a whole picture. Factually we, from long distances (from low-energy experiments with physical particles), penetrated to the end – to the point where bare particles live. Thus we insightful nailed the bare particle properties and their interaction laws correctly despite their hiding from us.
And yes, the bare non-interacting particles do interact and even self-interact. It is they who permanently do this hard work. At a first, naive, glance these statements are inconsistent, but no. It is a kind of duality in physics. This duality is not much advertised because the bare particles are really modest bricks.
(It’s a joke without humor.)