Casimir力在连续算子完备关系下的再推导
Rederivation of the Casimir force under the completeness relation of continuum operator
摘要：
卡西米尔效应表明，两个紧密相邻的平板，由于电磁场的量子真空涨落，通常会产生宏观吸引力。力的推导需要一个{ \it artificial}调节器，通过去除发散求和。通过自然地包括一个谱密度因子，基于观察到的不完整的本征向量，如自由场中的光子的本征态，可以形成一个完整的本征向量集通过引入一个独特的谱变换，提出了一种替代的方法来重新推导力，而不使用调节器。结果，Casimir力由第一项$-π^2 \hbar c/(240 a^4)$吸引，第二项$-π^4 \hbar c^3 σ^2/(1008 a^6)$也吸引，但较小，其中$a$为板间距，$σ$为谱密度因子中待确定的小常数。
英文摘要：
Casimir effects manifests that, the two closely paralleled plates, generally produce a macroscopic attractive force due to the quantum vacuum fluctuations of the electromagnetic fields. The derivation of the force requires an {\it artificial} regulator by removing the divergent summation. By including naturally a spectrum density factor, based on the observation that an incomplete eigenvectors of observable, such as the eigenstates for the photons in the free field, can form a complete set of eigenvectors by introducing a unique spectrum transformation, an alternative way is presented to rederive the force, without using a regulator. As a result, the Casimir forces are obtained with the first term $-π^2 \hbar c/(240 a^4)$ attractive, and the second one, $-π^4 \hbar c^3 σ^2/(1008 a^6)$, also attractive but smaller, with $a$ the plate separation, and $σ$ a to-be-determined small constant number in the spectrum density factor.
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