Krein空间量子化中的发散问题
A brief review on the Problem of Divergence in Krein Space Quantization
摘要：
本文对量子场论中的发散问题及其用Krein空间量子化方法消除作了简要的评述。该方法利用了辅助负频态，其模态不与物理状态发生相互作用，也不受物理边界条件的影响。值得注意的是，Krein空间量子化与Pauli-Villars正则化有相似之处，因此我们称之为“Krein正则化”。考虑Krein空间量子化的QED，可以证明该理论是自动正则化的。用Krein空间方法计算了真空极化、电子自能和顶点函数三个原始发散积分，由于红外和紫外发散没有出现，所以得到了有限值。再举一个例子，对于无质量的标量场，德西特时空中球壳上的卡西米尔应力可以用克莱因空间量子化来计算。
英文摘要：
In this paper we have a brief review on the problem of divergence in quantum field theory and its elimination using the method of Krein space quantization. In this method, the auxiliary negative frequency states have been utilized, the modes of which do not interact with the physical states and are not affected by the physical boundary conditions. It is remarkable that Krein space quantization is similar to Pauli-Villars regularization, so we can call it the "Krein regularization". Considering the QED in Krein space quantization, it could be shown that the theory is automatically regularized. Calculation of the three primitive divergent integrals, the vacuum polarization, electron self energy and vertex function using Krein space method leads to finite values, since the infrared and ultraviolet divergencies do not appear. For another example, the Casimir stress on a spherical shell in de Sitter spacetime for a massless scalar field could be calculated using Krein space quantization.
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