"Finite size effect"의 두 판 사이의 차이

2009년 8월 10일 (월) 01:21 판

Casimir effect in QED is one example of finite size effect
the stress on the bounding surfaces when quantum field is confined to finite volume of space
type of boundaries
- real material media
- interface between two different phases of the vacuum of a field theory such as QCD, in which case colored field may only exist in the interior region
- topology of space
the boundaries restrict the modes of the quantum fields
give rise to measurable and important forces
any kind of constraint or boudary conditions on the the zero-point modes of the quantum fields in question, including backgrounds such as gravity
In a model without boundary conditions, the Hamiltonian value associated wih the vacuum or ground state, called zero-point energy, is usually discarded because, despite being infinite, may be reabsorbed in a suitable redefinition of the energy origin
there are several ways to put such an adjustment into practice, normal ordering being oneof the most popular

\(z \to w=\frac{L}{2\pi}\ln z\)
energy momentum tensor changes
\(T_{cyl}(w)=(\frac{2\pi}{L})^2\{T_{pl}(z)z^2-\frac{c}{24}\}\)
\(L_0 \to L_0-c/24\)
the central charge emerges
central charge is proportional to the Casimir energy, the change in the vacuum energy density brought about by the periodicity condition on the cylinder

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 * Casimir effect in [[QED]] is one example of finite size effect
-* stree
+* the stress on the bounding surfaces when quantum field is confined to finite volume of space
+*  type of boundaries<br>
+** real material media
+** interface between two different phases of the vacuum of a field theory such as QCD, in which case colored field may only exist in the interior region
+** topology of space
+* the boundaries restrict the modes of the quantum fields
+* give rise to measurable and important forces
 * any kind of constraint or boudary conditions on the the zero-point modes of the quantum fields in question, including backgrounds such as gravity
 * In a model without boundary conditions, the Hamiltonian value associated wih the vacuum or ground state, called zero-point energy, is usually discarded because, despite being infinite, may be reabsorbed in a suitable redefinition of the energy origin
 * there are several ways to put such an adjustment into practice, normal ordering being oneof the most popular
+<h5>how to compute the Casimir effect</h5>
+* zero-point energy in the presenve of the boundaries
 *