论文标题
Casimir效应在Lorentz侵略标量场理论：一种局部方法
Casimir effect in Lorentz-violating scalar field theory: a local approach
论文作者
论文摘要
我们研究了两个平行导电板的经典几何形状中的Casimir效应，该板被距离$ l $隔开，用于标量场理论的破坏洛伦兹的扩展。该理论的洛伦兹（Lorentz）侵入部分的特征是$λ\ left（u \ cdot \ partial ϕ \ right） ^{2} $，其中参数$λ$和背景四矢量$ u ^μ$ codify codify codify lorentz对称性侵犯。我们使用Green的功能技术来研究板之间该区域真空应力能量张量的局部行为。获得Casimir能量和压力的封闭分析表达式。我们表明，能量密度$ \ MATHCAL {E} _ {C} $（因此，压力）可以用Lorentz-Invariant Energy Lenty Lenty Lenty $ \ Mathcal {E} _ {0} $表示，如下所示 \ Mathcal { $ \ tilde {l} = l / \ sqrt {1-λu_{n} ^{2}} $是一个重新固定的板到板间隔，而$ u_ {n} $是$ \ vec {u} $的组件，沿正常情况。像往常一样，局部Casimir能量的分歧不会导致压力。
We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $λ\left( u \cdot \partial ϕ\right )^{2}$, where the parameter $λ$ and the background four-vector $u ^μ$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density $\mathcal{E}_{C}$ (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density $\mathcal{E}_{0}$ as follows \begin{align} \mathcal{E}_{C} (L) = \sqrt{\frac{1-λu_{n} ^{2}}{1 + λu ^{2}}} \mathcal{E}_{0} (\tilde{L}) , \notag \end{align} where $\tilde{L} = L / \sqrt{1-λu_{n} ^{2}}$ is a rescaled plate-to-plate separation and $u_{n}$ is the component of $\vec{u}$ along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.
