Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
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局部和全局卡西米尔能量：发散、重正化以及与引力的耦合
DOI：
10.1007/978-3-642-20288-9_3
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Milton
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文献类型：
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作者：
K. Milton
从这门学科开始，量子真空能量或卡西米尔能量的计算就一直受到两种发散的困扰：总能量，可以被认为是零点能量的某种正则化，\（\sum\frac{1}{ 2}\hbar\omega，\）似乎明显发散。从能量-动量张量的真空期望值\（\langle T_{00}\rangle\）得到的局域能量密度通常在边界附近发散。这两种类型的分歧彼此关系不大。任何类型的不同刚体之间的相互作用的能量是有限的，对应于物体之间可观察到的力和扭矩，可以明确计算。当刚体的相对位置改变时，表面附近发散的局部能量密度不改变。一个物体的自我能量是不太明确的，并遭受分歧，这可能是或可能不是可消除的。一些例子，其中一个独特的总自应力可以评估包括理想的导电球壳第一次考虑的博耶，一个理想的导电圆柱壳，和稀释的电介质球和圆柱。在这些情况下，有限部分是唯一的，但也有不同的贡献，可以归入某种形式的重整化的物理参数。自能的有限性与效应的物理可观测性问题是分开的。在表面附近的局部能量-动量张量中发生的发散与总能量中的发散不同，总能量中的发散通常与精确位于表面上的能量有关。然而，局域能量-动量张量与引力耦合，那么这里的无穷大量有什么意义呢？对于平行板的经典情况，有迹象表明，局部能量密度的发散与爱因斯坦方程的发散是一致的;相应地，已经表明，总卡西米尔能量的发散可以根据等效原理精确地重新归一化板的质量。这应该是一个普遍的性质，但还没有建立，例如，对于Boyer球。众所周知，这种局部的分歧对宏观因果关系没有影响。
From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, \(\sum\frac{1}{ 2}\hbar\omega,\) seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, \(\langle T_{00}\rangle ,\) typically diverge near boundaries. These two types of divergences have little to do with each other. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The divergent local energy densities near surfaces do not change when the relative position of the rigid bodies is altered. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The finiteness of self-energies is separate from the issue of the physical observability of the effect. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein’s equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle. This should be a general property, but has not yet been established, for example, for the Boyer sphere. It is known that such local divergences can have no effect on macroscopic causality.