# Why can we believe the value of field is fluctuated?

1. Feb 4, 2016

### fxdung

What is the basis for the believe that the value of field is fluctuated at micro-level?Does the existence of photons demontrate the need of express field in form of operators then deducing the fluctuation of quantum field through Heizenberg commutators?

Last edited: Feb 4, 2016
2. Feb 5, 2016

### fxdung

Does we not need or we can not quantize the statistic electric fields?

3. Feb 5, 2016

### stevendaryl

Staff Emeritus
Well, for any measurable quantity $A$, we can get an estimate of how much it varies by computing the variance: $var(A) = \langle A^2 \rangle - \langle A \rangle^2$, where $\langle \rangle$ means taking the expected, or average, value. In vacuum, in the absence of any charges, we can compute $\langle \vec{E}\rangle$, the expected value of the electric field, and we find it's zero. But the computation for $\langle E^2 \rangle$ is not zero, or at least, is not obviously zero. (I believe the naive way of computing it results in an infinite value, which of course, makes no sense. I'm not sure what a more careful analysis yields.)

Last edited: Feb 5, 2016
4. Feb 5, 2016

### fxdung

In the present of charges,existing the longitudinal electric field(statistic field).Why we do not consider the quantization of the fields?Classically the field is Coulomb field,but how is it if we consider ''the corresponding quantum fields''?

5. Feb 5, 2016

### A. Neumaier

The notion of unpolarized light cannot even be expressed in terms of non-fluctuating fields.

6. Feb 5, 2016

### A. Neumaier

In QED, the whole electromagnetic field is quantized. But what one sees when starting from the Fock space is only the noninteracting (asymptotic) piece, where the longitudinal part of the field vanishes. The remaining part is created by the interaction, which modifies all field operators.

7. Feb 6, 2016

### fxdung

I am confused between three following ideas:
-Particles is product of exciting state of field.But what is the exciting states?
-Field is a huge cluster of many particles between them have exchange interaction and that the number of particles can be fluctuated.Electromagnetic field is a ''set''of photons.
-Particle is a packet of field.But why the particle is a point particle?
Which idea is correct or the all are correct?

Last edited: Feb 6, 2016
8. Feb 7, 2016

### fxdung

I have heard that there is not concept about probability of photon at a position.So photon concept has global character.Then I think that the packet of field of a quantum field(photon) carries the point particle(or point photon) and then having not the Heizenberg relation between position and momentum when the mass of particle is zero.
Quantum mechanics for zero mass particle has not position representaion.It is the answer for my question above.Is it correct?

9. Feb 8, 2016

Yes.