Free Field Vacuum: What Does It Correspond To?

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SUMMARY

The discussion centers on the concept of free field vacuum in quantum field theory, particularly in the context of phi^4 theory and quantum electrodynamics (QED). Participants explore whether the free field vacuum corresponds to a state devoid of particles, suggesting it may be represented by the null Feynman diagram, which lacks vertices or propagators. The conversation also touches on vacuum fluctuations and the implications of the uncertainty principle, with one participant asserting that a true vacuum is simply empty space without any particle interactions.

PREREQUISITES
  • Understanding of quantum field theory concepts, particularly phi^4 theory and QED.
  • Familiarity with Feynman diagrams and their significance in particle physics.
  • Knowledge of vacuum fluctuations and the uncertainty principle in quantum mechanics.
  • Basic comprehension of particle-antiparticle pair production and annihilation processes.
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  • Research the implications of vacuum fluctuations in quantum field theory.
  • Study the role of the uncertainty principle in particle physics.
  • Examine the significance of the null Feynman diagram in theoretical physics.
  • Explore the article "Clothed particle operators in simple models of quantum field theory" by O. W. Greenberg and S. S. Schweber for deeper insights.
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Physicists, students of quantum field theory, and researchers interested in the foundational concepts of vacuum states and particle interactions in theoretical physics.

Neitrino
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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
 
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a bubble with no external legs?
 
Neitrino said:
To what does the free (non-interacting) field vacuum correspond?
Does such a thing even exist?
 
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...
 
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}.
 
May be in other words my question will sound what are the free field vacuum fluctuations...
 
Any additional comments?
 
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.
 

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