I'm trying to develop an intuition about quantum fields. It seems to me that a quantum field cannot be anything like a classical field. If the field is connected and continuous, then you'd expect that any disturbance would have to propagate in all directions and thus any "particle" would have to almost immediately dissipate, right? Or if a field were a piecewise linear thing, where disturbances are discrete, then wouldn't that still require disturbances to dissipate? In fact it would dissipate more quickly since there would come a point where the dissipating wave would not have enough of an effect on its neighborhood to change the next portion by the minimum discrete value. So it would cease to propagate at that point. So I'm thinking that particles cannot be disturbances of any kind of connected field, since that would require that particles dissipate. And unconnected fields cannot propagate through absolutely nothing. So instead I'm thinking that particles must therefore be the absence of a connected field, places where the field (or spacetime) no longer exists. These are places where spacetime (or at least the field) comes to a boundary. A boundary does not dissipate. Am I right on that point? Then the field only describes the average density of such particles, the probability of finding a particle at a given point.