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I believe there are cases where they are observable. Especially through their effects. In cosmology, for example, quantum fluctuations in the early inflationary epoch are considered to have seeded the large scale structure of the universe.
In a more 'accessible' example, quantum fluctuations are the cause of the Casimir effect, which can be measured. In this ...
2
Since this is a log-log plot the straight lines (Coulomb, gravitation, strong inside $10^{-15}$ m) are the long range power laws ($1/r$) resulting from exchange of massless bosons (photon, gluon, graviton). I'm not sure what units are being used for the vertical (potential) axis but it is probably eV or MeV (hard to tell on a log-log plot). For the weak ...
2
The dynamics of the theory do not depend on the state. So if the Hamiltonian contains interaction terms, these terms are still there in a vacuum.
Here's a way you could quantify the effect of the interactions. Imagine you need to compute a 2-point correlation function between a field $\phi_1$ at spacetime point $\{x_1,t_1\}$ and $\phi_2$ at $\{x_2,t_2\}$ in ...
2
Beware that you'll need to perform the backwards transformation in 3D Fourier space -- for the photon field $p^2 = 0$, thus your original expression to start from does not make a lot of sense. Apart from that, the classical Coulomb field does not depend on time, which in another hint for the 3D transformation.
In Schwartz's book, this is done in Ch. 3.4.2 (...
1
The Lamb Shift is pretty much considered to be the 1st observation of quantum fluctuations. It is a small energy difference between the $^2S_{\frac 1 2}$ and $^2P_{\frac 1 2}$ states in the hydrogen atom.
The relativistic theory of the electron, the Dirac equation, predicts that the electron binding energies in these two states have the same energy (so-...
1
If you use lattice formalism of gauge theory, defining all that Wilson action and related objects, you can obtain asymptotic form of the potential by calculating the expectation value of Wilson loop.
Then for strong coupling limit (where we do strong coupling expansion), even in QED(single abelian or U(1)), you get linearly rising term.
However in weak ...
1
$$\begin{align}{\rm Det} \left(\frac{\delta G}{\delta \alpha}\right)
~=~&\int {\cal D}c{\cal D}\bar{c}\exp\left(\int \!d^4x \int \!d^4y ~\bar{c}(x)\frac{\delta G(x)}{\delta \alpha(y)}c(y) \right) \cr
~=~&\int {\cal D}c{\cal D}\bar{c}\exp\left(\int \!d^4x \int \!d^4y ~\bar{c}(x) \frac{1}{e}\partial_x^2\delta(x-y) c(y) \right)\cr
~=~& {\rm Det} \...
1
yes, but in quantum theory the word 'static' here means that there is no evolution over time (except a global phase), it does not mean that a sequence of observations will all yield the same result
yes; 'indivisible' in the sense that it is continuous and you can't separate one part from another so as to leave a hole where there is no quantum field
yes, ...
1
For example, if a red traffic light is shining at 700nm, does each photon have 'quatum wavelength' of 700nm
yes
Does this mean that (for a given instant in time) the probability of detecting said photon rises and falls every 700nm?
Yes, if the wave is plane polarized, so that the classical energy density has this oscillation. The probability density has ...
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