论文标题
洛伦兹违反标量casimir效应的$ d $维度球
Lorentz violating scalar Casimir effect for a $D$-dimensional sphere
论文作者
论文摘要
我们研究了Casimir效应，这是由于标量场在$ d $维的球体中限制，洛伦兹对称性破坏了。该理论的Lorentz-violation部分由术语$λ（u \ cdot \ partial ϕ） ^{2} $描述，其中参数$λ$和背景矢量$ u ^μ$编码Lorentz Symmetry的分解。我们计算，作为$ d $的函数，Casimir通过使用Green的功能技术来对向量$ u ^μ$进行两种特定选择。在及时的情况下，$ u ^μ=（1,0，...，0）$，可以将Casimir应力分解为Lorentz不变结果的乘积因子$（1 +λ） ^{ - 1/2} $。对于径向间距的情况，$ u ^μ=（0,1,0，...，0）$，我们获得了Casimir应力的分析表达式，尽管如此，该表达式仍未接受lorentz不变结果的分解。对于径向空间的情况，我们发现存在一个临界值$λ_{c} =λ_{c}（d）$，casimir应力从排斥行为转变为任何$ d> 2 $的有吸引力的行为。详细分析了与物理相关的情况$ d = 3 $，其中找到了临界值$λ_{c} | _ {\ small d = 3} = 0.0025 $。与Lorentz对称情况一样，该部队以正整数为$ d $的差异行为。
We investigate the Casimir effect, due to the confinement of a scalar field in a $D$-dimensional sphere, with Lorentz symmetry breaking. The Lorentz-violating part of the theory is described by the term $λ(u \cdot \partial ϕ) ^{2}$, where the parameter $λ$ and the background vector $u^μ$ codify the breakdown of Lorentz symmetry. We compute, as a function of $D$, the Casimir stress by using Green's function techniques for two specific choices of the vector $u ^μ$. In the timelike case, $u ^μ = (1,0,...,0)$, the Casimir stress can be factorized as the product of the Lorentz invariant result times the factor $(1 + λ) ^{-1/2}$. For the radial spacelike case, $u ^μ = (0,1,0,...,0)$, we obtain an analytical expression for the Casimir stress which nevertheless does not admit a factorization in terms of the Lorentz invariant result. For the radial spacelike case we find that there exists a critical value $λ_{c} = λ_{c} (D)$ at which the Casimir stress transits from a repulsive behavior to an attractive one for any $D> 2$. The physically relevant case $D = 3$ is analyzed in detail where the critical value $λ_{c}|_{\small D=3} = 0.0025$ was found. As in the Lorentz symmetric case, the force maintains the divergent behavior at positive even integer values of $D$.
