# I Can Quantum Fields be derived from Particles?

1. Apr 6, 2017

### friend

Typically, particles are said to be excitations of quantum fields. My question is whether fields can be derived from particles. Perhaps virtual particles can be summed up in some way to produce a field, for example. Any theories on this? Thanks.

2. Apr 6, 2017

### atyy

For interacting fields - technically no, but physics thinking says yes.

As an example of physics thinking, see the Nair and Weinberg QFT texts.

Physics thinking is that it's ok to be wrong, as along as experiment shows we are right :)

3. Apr 7, 2017

### A. Neumaier

In order to get free quantum fields from noninteracting particles you need to assume that the number of particles can be arbitrary. Then the process is called second quantization. For interacting theories it only works in the nonrelativistic case.

In the relativistic case one has problems with defining the interactions, which are far too singular to be represented in a pure particle framework.

4. Apr 7, 2017

### Demystifier

In perturbative string theory, one usually starts from strings (which can be thought as "particles" slightly extended in one dimension), calculates the scattering amplitude from first quantization of strings, then makes a limit in which the string extension is put to zero, and finally identifies the corresponding effective field theory which gives the same scattering amplitude. Schematically, this chain of reasoning can be written as
string -> particle -> field

5. Apr 7, 2017

### A. Neumaier

where is this done?

6. Apr 7, 2017

### Demystifier

Last edited by a moderator: May 8, 2017
7. Apr 7, 2017

### A. Neumaier

They only identify which effective theory matches the predictions. For this it is enough to produce an effective theory that agrees.

But this does not mean that the field theory is constructed from the particle theory. The effective theory must be constructed independently!!

8. Apr 7, 2017

### Demystifier

What would you say about the Feynman original construction of Feynman diagrams? He constructed them without really using field theory. And for that matter, what do you think about Feynman rules as introduced in Bjorken Drell 1?

9. Apr 7, 2017

### A. Neumaier

Without a Lagrangian (and hence a field theory) no Feynman rules!

10. Apr 8, 2017

### Denis

I think QFT on curved background is a good argument that it is the field which is more fundamental.

Field theoretic picture: We have a field. The equation of evolution of the field changes, in dependence of the gravitational background. But the ontology does not change at all. The field is the same, some function $\varphi(x, t)$.

Particle picture: Even the state which does not contain any particles - the vacuum - changes with time. So, there can be no time-independent particle ontology at all.

11. Apr 8, 2017

### vanhees71

Bjorken&Drell 1 shouldn't be used today anymore (while Bjorken&Drell 2 has one of the best treatments of the tricky issue of asymptotic free states, LSZ, and all that; the only caveat is that it was written before all quibbles with overlapping divergences in the renormalization procedure were fully understood, so that you should use a more modern text when it comes to renormalization).

Feynman's original construction of Feynman diagrams was something only he could do. That's just the right educated guess of a genius. We normal mortals are glad to have had Dyson, combining QFT a la Schwinger and Tomonaga with Feynman's digram techniques, i.e., deriving the Feynman rules from QFT, so that we can understand Feynman's procedure from a clear formalism (QFT).

12. Apr 9, 2017

### friend

Can the derivation be worked backwards from Feynman rules to QFT? If not, why not? Thanks.

13. Apr 10, 2017

### ftr

I think the main problem is that although the electron(QED) emits/absorbs the "virtual photon" (i.e. they seem to be integral to each other) the formalism still insists on two fields electron and EM. Split like that already the electron particle picture all gone to pieces(no pun intended)