hellfire

Science Advisor

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- 1

## Main Question or Discussion Point

I am confused with the Scharnhorst and Casimir effects. The confusion started here. As it seams that there is no response to my questions in post #9, I will try here.

I stated there my understanding about perturbation theory which leads to Feynman diagrams: The amplitudes for the fluctuations in the vacuum state of a free field can be computed as a time ordered product of fields in <0|…|0>. According to Wick's theorem, this can be decomposed as a product of Feynman propagators, leading to Feynman diagrams with no loops. Only if an interaction exists, a term [tex]e^{-i\int dt H_I}[/tex] appears within the product <0|...|0> due to the fact that one does not consider |0> anymore but the vacuum state of an interacting field expressed in terms of |0>. Only the term with the integral leads to loops in the Feynman diagrams after expanding the exponential as a power series (this is basically what I understood from P&S).

I think this summarizes to the statement that virtual particles appear only in case of interactions. However, what I wrote above seams to be incorrect. Otherwise, claims like this:

I stated there my understanding about perturbation theory which leads to Feynman diagrams: The amplitudes for the fluctuations in the vacuum state of a free field can be computed as a time ordered product of fields in <0|…|0>. According to Wick's theorem, this can be decomposed as a product of Feynman propagators, leading to Feynman diagrams with no loops. Only if an interaction exists, a term [tex]e^{-i\int dt H_I}[/tex] appears within the product <0|...|0> due to the fact that one does not consider |0> anymore but the vacuum state of an interacting field expressed in terms of |0>. Only the term with the integral leads to loops in the Feynman diagrams after expanding the exponential as a power series (this is basically what I understood from P&S).

I think this summarizes to the statement that virtual particles appear only in case of interactions. However, what I wrote above seams to be incorrect. Otherwise, claims like this:

Make no sense to me. As far as I know the EM field inside the plates of a Casimir effect is not interacting. Phenomena like the Scharnhorst effect (FTL of photons in a Casimir vacuum) make also no sense as it seams to imply that there is some contribution of virtual particles to the propagation of light in a normal free vacuum (a contribution which is smaller in the Casimir vacuum).Wikipedia said:The Casimir effect and Hawking radiation are examples of phenomena whose existence can be proved using one-loop Feynman diagrams.