Vacuum energy and Casimir effect

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http://bomber0.myid.net/ (토론)님의 2009년 12월 31일 (목) 17:33 판 (피타고라스님이 이 페이지의 위치를 <a href="/pages/4899611">0 수리물리</a>페이지로 이동하였습니다.)
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vacuum energy
  • ground state energy
  • vacuum state energy
  • zero point energy

 

 

QFT and the vacuum amplitude
  • In QFT, there is a way to relate the vacuum energy density with the vacuum amplitutde.
  • QFT provides ways to compute the vacuum amplitude.
  • Sometimes it is related to the zeta values.

 

Vacuum energy density
  • We can measure the Vacuum energy density by cosmological microwave background.
  • a non-zero vacuum energy is expected to contribute to the cosmological constant, which affects the expansion of the universe.

 

 

  • Casimir effect
  • central charge

 

 

Vacuum energy and L-values

Let \(\chi \colon(\mathbb{Z}/n\mathbb{Z})^\times \to \mathbb C^{*}\) has the conductor f.

\(L(-1, \chi) = \frac{1}{2f}\sum_{n=1}^{\infty}{\chi(n)}{n}\)

As the shift \(L_0 \to L_0-\frac{c}{24}\) has the effect of cancelling the linear term in the commutation relation, we do \(L_0^{\ \chi} \to L_0^{ \chi}+\frac{1}{2f}L(-1, \chi)\) to get

 

 

 

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