Free Field Vacuum: What Does It Correspond To?

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Discussion Overview

The discussion centers around the nature of the free (non-interacting) field vacuum in quantum field theory, particularly in relation to interacting field theories such as phi^4 theory and quantum electrodynamics (QED). Participants explore concepts of vacuum fluctuations, the structure of the vacuum, and the implications of these ideas in theoretical physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions what the free field vacuum corresponds to, suggesting it may be analogous to bubbles in interacting theories.
  • Another participant proposes the idea of a "bubble with no external legs" as a potential representation of the free field vacuum.
  • A different participant expresses skepticism about the existence of a free field vacuum, questioning its physical reality.
  • One contributor discusses the notion that the free field vacuum may consist of propagating particles that emerge and disappear within a time frame that does not violate energy conservation, invoking the uncertainty principle.
  • Another participant describes the free field vacuum as represented by the null Feynman diagram, which lacks vertices or propagators, and relates it to vacuum expectation values.
  • A participant seeks clarification on the concept of free field vacuum fluctuations.
  • One participant asserts that, in their view, the vacuum is simply empty space without any particles or fluctuations, criticizing theories that suggest otherwise.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the free field vacuum, with some proposing it contains fluctuations and others arguing it is devoid of any physical entities. The discussion remains unresolved with multiple competing perspectives present.

Contextual Notes

Participants reference various theoretical constructs and implications, but there are limitations in the assumptions made regarding the nature of the vacuum and its physical interpretation. The discussion does not resolve the complexities surrounding these concepts.

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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