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arXiv 1209.5237hep-th
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耦合费米子-孤子系统的Casimir能量

Casimir Energy for a Coupled Fermion-Soliton System

Leila Shahkarami, Azadeh Mohammadi, Siamak Sadat Gousheh

备注：
11 pages, 6 figures
发表信息：
JHEP 1111:140,2011
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摘要：

本文计算了费米子-赝标耦合场系统的Casimir能量。在本文所考虑的模型中，赝标场是具有两个可调参数的\textit{static}和\textit{prescribed}。这些参数确定了无穷远处的场值（$\pm θ_0$）及其变化尺度（$μ$）。通过改变$θ_0$可以建立任意拓扑荷的场组态，通过改变$μ$可以在极端绝热和非绝热状态之间进行插值。这个系统是完全可解的，因此我们通过使用能量密度减法方案来精确和明确地计算Casimir能量。我们表明，在一般情况下，Casimir能量在极端绝热极限为零，并在极端非绝热极限时，赝标场的渐近值正确对应于一个配置与任意拓扑电荷。此外，在一般情况下，Casimir能量总是积极的和平均的$θ_0$的递增函数，总是有局部最大值时，有一个零模式，表明这些配置是积极的不利。我们还计算和显示的能量密度与光谱亏损的连续，和那些束缚态。我们表明，与$E>0$和$E<0$的状态的光谱的失真的能量密度是彼此的镜像。我们还计算和显示了Casimir能量密度。最后计算了一个孤立子和一个价电子组成的系统的能量，并证明了该系统的Casimir能量与束缚能具有可比性。

英文摘要：

In this paper we compute the Casimir energy for a coupled fermion-pseudoscalar field system. In the model considered in this paper the pseudoscalar field is \textit{static} and \textit{prescribed} with two adjustable parameters. These parameters determine the values of the field at infinity ($\pm θ_0$) and its scale of variation ($μ$). One can build up a field configuration with arbitrary topological charge by changing $θ_0$, and interpolate between the extreme adiabatic and non-adiabatic regimes by changing $μ$. This system is exactly solvable and therefore we compute the Casimir energy exactly and unambiguously by using an energy density subtraction scheme. We show that in general the Casimir energy goes to zero in the extreme adiabatic limit, and in the extreme non-adiabatic limit when the asymptotic values of the pseudoscalar field properly correspond to a configuration with an arbitrary topological charge. Moreover, in general the Casimir energy is always positive and on the average an increasing function of $θ_0$ and always has local maxima when there is a zero mode, showing that these configurations are energetically unfavorable. We also compute and display the energy densities associated with the spectral deficiencies in both of the continua, and those of the bound states. We show that the energy densities associated with the distortion of the spectrum of the states with $E>0$ and $E<0$ are mirror images of each other. We also compute and display the Casimir energy density. Finally we compute the energy of a system consisting of a soliton and a valance electron and show that the Casimir energy of the system is comparable with the binding energy.

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