论文标题
同心$δ$ - $δ'$ spheres的Casimir Energy
Casimir Energy for concentric $δ$-$δ'$ spheres
论文作者
论文摘要
我们研究标量场和两个同心球的真空相互作用，其表面上的奇异电位定义。电势是Dirac-$δ$及其衍生物的线性组合。从球体内部或从球体的外部看到时，三角洲素数的存在在潜在原因中的表现不同。我们研究了不同的案例，以达到三角洲素耦合的正值和负值，从而使三角洲的耦合保持阳性。结果，我们发现能量为正，负或零的耦合空间中的区域。此外，$δ'$耦合的符号在RADII的不同值的Casimir Energy上导致不同的行为。这种电势会产生一般的边界条件，并限制了定义Dirichlet和Robin边界条件的局限性，这使我们能够模拟纯电o纯电磁球。
We study the vacuum interaction of a scalar field and two concentric spheres defined by a singular potential on their surfaces. The potential is a linear combination of the Dirac-$δ$ and its derivative. The presence of the delta prime term in the potential causes that it behaves differently when it is seen from the inside or from the outside of the sphere. We study different cases for positive and negative values of the delta prime coupling, keeping positive the coupling of the delta. As a consequence, we find regions in the space of couplings, where the energy is positive, negative or zero. Moreover, the sign of the $δ'$ couplings cause different behavior on the value of the Casimir energy for different values of the radii. This potential gives rise to general boundary conditions with limiting cases defining Dirichlet and Robin boundary conditions what allows us to simulate purely electric o purely magnetic spheres.
