Free Field Vacuum: What Does It Correspond To?

[Neitrino]

Hello PF,

If the the interacting field (phi^4 theory or QED) vacuum corresponds to bubbles for example: photon goes into electron-positron pair and then vice versa.. etc... etc...

To what does the free (non-interacting) field vacuum correspond?

10x

 

[ansgar]

a bubble with no external legs?

 

[bapowell]

To what does the free (non-interacting) field vacuum correspond?

Does such a thing even exist?

 

[Neitrino]

Since the only structure that can be constructed for free field is its propagator can we say that process of birth is real death is real but all this happens in a tiny time interval that no energy violation is detected... If there were charges for example electric of course antiparticle will do the same.

But basically can we say that a free field vacuum consists of propagating particles that just emerge-propagate-disappear-emerge-propagate-disappear and energy violation is not detected (which in this case may mean that really nothing is happening) due to uncertainty principle?

And the bubble is certain case where coordinates are equal...


Am I in a dark dark forest...

 

[DarMM]

The free field vacuum is just the null Feynman diagram/graph. That is the diagram with no verticies or propagators.

Although technically speaking the Feynman diagrams describe the vacuum expectation values, so the null Feynman diagram/graph is actually the inner product
$$\left(\Omega_{0},\Omega_{0}\right)$$. The free field vacuum is the state $$\Omega_{0}$$.

 

[Neitrino]

May be in other words my question will sound what are the free field vacuum fluctuations...

 

[Neitrino]

Any additional comments?

 

[meopemuk]

Neitrino,

In my personal opinion, vacuum is just empty space. There can be no particles, bubbles, electron-positron pairs etc. in real physical vacuum. If a theory (phi^4 for example) tells you otherwise, then it is bad, unphysical theory.

I highly recommend this article:

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim., 8 (1958), 378.

Eugene.