# What is a Quantum Field?

1. Jun 1, 2004

### Mike2

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.

2. Jun 1, 2004

### slyboy

In quantum field theory, particles are a particular type of excitiation of a continuous filed. They do tend to spread out during dynamical evolution, just as Schroedinger wave packets do in the non-relativistic theory. It is no more problematic in field theory than it is in ordinary quantum mechanics. However, this is not saying much because it is very problematic in ordinary quantum mechanics and is related to the measurement problem.

3. Jun 1, 2004

### Mike2

So are you saying that the problem is that the wave disperses but the particle does not?

4. Jun 2, 2004

### slyboy

The wave always disperses, but a particle is only ever detected at points. The probabilities for detection at different points are given by the Born rule and the wavefunction collapses after the detection. The measurement problem is concerned with how all this can be made compatible.

5. Jun 2, 2004

### Mike2

My point is that if the wave function only describes the probability density of finding a particle, then it is not a field whose disturbance IS the particle. The wave function is an alternative field only used as an alternative discription. It is not the field whose disturbance describes the nature of the particle itself. The wave function is only an added description.

6. Jun 2, 2004

Staff Emeritus
I don't know why physicists don't pay more attentions to solitons. These nonlinear excitations do not disperse (dispersion is countered by nonlinear effects) and they are capable of superposition, etc.

7. Jun 2, 2004

### Mike2

OK, so let me see if I understand you right. You're saying that the soliton is a disturbance of some field which does not dissipate in all direction. And this is not the "wave function" which only gives the alternate description of the probability of finding the particle somewhere, right?

I'm under the impression that disturbances dissipate in all directions simply because the field is connected. But you are saying that there is a connected field that does not dissipate, right? I can't imagine how nonlinearity could prevent dissipation. Would appreciate your insights on this. Thanks.

8. Jun 3, 2004

### slyboy

It is certainly correct that solitons do dont dissipate, but the particle solutions of quantum field theory are not solitons. It would be intruiging to see if one could come up with a variant of QFT that did use solitons, but I don't think it would be easy to cope with phenomena such as tunnelling. Perhaps solitons could play a role in the classical limit of quantum mechanics.

9. Jun 3, 2004

### setAI

Last edited: Jun 3, 2004