Apologies in advance for the possible vagueness of my question. If it is not a good question, an explanation of why it isn't would be a very useful answer to me.
I am trying to find a useful mental picture of interactions in QFT. I think these kinds of mental pictures are an indispensable aid to grasp abstract concepts in some intuitive way that can guide you when doing hard calculations, but when the picture is inaccurate it can also lead you astray.
I have seen as the mental picture of interactions by particle exchange in QFT two people throwing a ball back and forth, resulting in a repulsive force. For attractive forces, they either throw a boomerang, or a ball with negative momentum.
I don't really see how this picture actually can guide us in any meaningful way, though maybe that is because I don't understand QFT well enough.
I was thinking that maybe a useful picture would be to still think in terms of point particles, but their interaction is through a field, as required by locality. In fact, both particles interact with the field, rather than directly with each other. Since this is a quantum field, changes in the field are quantized: the change is interpreted as the addition of a particle to the field, or the absorption of a particle from the field. If this picture is more or less correct, interacting particles don't really exchange particles, but rather they both interact with the boson field, thereby altering it, which will in turn do something to the other particle.
However, I think this cannot be really accurate: the particles added to the field or absorbed from it are virtual, hence they are not observable: they cannot originate from only one particle interacting with the field: unless a disturbance created by one particle is absorbed by the other, it was never really there. If there is any validity to the previous description, is there any way it can be made more accurate to account for the non-observability of the exchanged bosons?
Another refinement would be not to imagine the interacting particles as some classical kind of point particles, but rather as the quanta of disturbance of their own fields. In the straightforward picture it is not hard to imagine any kind of interaction, but it is not so clear what would be the role of a force-mediating field.
As a particular application I would be interested how asymptotic freedom in QCD could be imagined in terms of such a picture. Should be first translate high energy to short distance (only in the first picture in which the particles are points)? If so, can we see what it would mean that the coupling is low at very short separations? Or should be see the high energy as the matter field disturbance to consist of very high frequency fluctuations, and can we see what it means that at high frequencies the fields interact little?
Is there any validity to these mental pictures? If so, which one would be most accurate, and how could it be corrected or refined?