A Vacuum pair creations on the light-cone

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When a field is quantized on the light front, there is no possible pair creation from the vacuum energy. This is because kinematic operator P^+ generates only a positive spectrum ( https://en.wikipedia.org/wiki/Light_front_quantization#Spectral_condition ). So there is no "particles popping out of the Dirac Sea." I have been looking for an intuitive explanation for this. Does someone knows of one?
 

vanhees71

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The intuitive explanation is that nothing ever is "popping out of the vacuum". The vacuum is nothing, and nothing can pop out of nothing. There's also no Dirac sea. It's just gotten rid of by normal ordering in the operator formalism or by renormalization of the total charge and and total energy, momentum, and angular momentum of the vacuum (all of these quantities are set to 0 in the vacuum state). Dirac's hole-theoretic formulation of QED is fortunately overcome by modern formulations of QFT.

Any other claim is just popular-science confusion for the public (which in fact deserves better explanations by scientists, because after all the tax payers are funding most of the fundamental research we do all over the world!). Also have a look at the newest Insights article:

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/
 
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The intuitive explanation is that nothing ever is "popping out of the vacuum". The vacuum is nothing, and nothing can pop out of nothing. There's also no Dirac sea. It's just gotten rid of by normal ordering in the operator formalism or by renormalization of the total charge and and total energy, momentum, and angular momentum of the vacuum (all of these quantities are set to 0 in the vacuum state). Dirac's hole-theoretic formulation of QED is fortunately overcome by modern formulations of QFT.

Any other claim is just popular-science confusion for the public (which in fact deserves better explanations by scientists, because after all the tax payers are funding most of the fundamental research we do all over the world!). Also have a look at the newest Insights article:

https://www.physicsforums.com/insights/vacuum-fluctuation-myth/
Right, the language of Dirac sea is outdated, which is why I put it in quote. I am sorry for using an old image. But surely, that there are virtual particle creations out the vacuum, which can be materialized if a field is present, is still a fact: That is the basis for the Casimir effect, people go to great (CPU-)pain to add disconnected diagrams when the do lattice computation, etc... The textbook from which I learned QFT is fairly modern (Zee's QFT in a nutshell) and does discuss vacuum fluctuations. These diagrams complicates terribly the calculations and that's why some choose to work on the light-front rather than the instant-front, although the light front is not as intuitive as the instant one (and has other drawbacks). So to rephrase my question, is there an intuitive explanation of why there is no effect of vacuum fluctuations on the light front, while we have to account for these effects on other front forms?
 

Vanadium 50

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there are virtual particle creations out the vacuum, which can be materialized if a field is present, is still a fact: That is the basis for the Casimir effect
Not true.
 
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Not true.
You are right, I was thinking of Schwinger pair creations. Apologies. I see also that the Casimir effect is not interpreted anymore in term of vacuum energy. Things have evolved since I learned about QFT...
 
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vanhees71

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You are right, I was thinking of Schwinger pair creations. Apologies. I see also that the Casimir effect is not interpreted anymore in term of vacuum energy. Things have evolved since I learned about QFT...
It's not true either. The Schwinger effect describes spontaneous pair creation due to a strong electromagnetic field. That's far from being vacuum!
 
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It's not true either. The Schwinger effect describes spontaneous pair creation due to a strong electromagnetic field. That's far from being vacuum!
That is of course what I mean: pair creations under large electric fields, which is why I brought it up in the context of the Casimir effect. The usual interpretation is as pair creation from vacuum . The pair got separated by a large enough electric field. The "borrowed" energy of the virtual pair creations is paid back by the electric field.
see e.g. http://www.qgf.uni-jena.de/gk_quantenmedia/Texte/hebenstreit090623-p-61.pdf
 

vanhees71

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It is NOT "the usual interpretation". It's repeated over and over again in popular-science textbooks. The standard derivation goes back to Schwinger and it's just the nonperturbative transition amplitude from the vacuum to an electron-positron pair due to a strong electric (in this first calculation electrostatic homogeneous) field, and this is not vacuum. The vacuum itself is stable and Poincare invariant. Nothing pops out of nothing. In the cited talk by Florian Hebenstreit it's indeed explicitly treated with standard QED, not with nonsensical "something-poping-out-of-nothing" narratives used by lazy popular-science book authors!
 

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