偶极量子化与二维共形场论的无限圆周极限
Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
摘要：
在我们前面的介绍中，引入了{ \it偶极量子化}项，我们在这里论证了采用$L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$而不是$L_0+{\bar L}_0$作为哈密顿量在二维共形场论中产生无限周长极限。新的哈密顿量导致偶极量子化而不是径向量子化。结果表明，除了具有连续指标的维拉索罗代数外，新理论还具有连续的强退化谱.它的希尔伯特空间表现出一个不同的内积比原来的理论。这个特殊的哈密顿量的特质是它与所谓的正弦平方变形的关系，这是在研究某类量子统计系统时发现的。无限周长的出现解释了为什么正弦平方形变系统的真空态与相应的闭边界系统的真空态重合。
英文摘要：
Elaborating on our previous presentation, where the term {\it dipolar quantization} was introduced, we argue here that adopting $L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$ as the Hamiltonian instead of $L_0+{\bar L}_0$ yields an infinite circumference limit in two-dimensional conformal field theory. The new Hamiltonian leads to dipolar quantization instead of radial quantization. As a result, the new theory exhibits a continuous and strongly degenerated spectrum in addition to the Virasoro algebra with a continuous index. Its Hilbert space exhibits a different inner product than that obtained in the original theory. The idiosyncrasy of this particular Hamiltonian is its relation to the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The appearance of the infinite circumference explains why the vacuum states of sine-square deformed systems are coincident with those of the respective closed-boundary systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
