非交换空间中的阈值局部化
Localization at threshold in noncommutative space
摘要：
标度对称系统的基态能量通常不具有任何下界，从而使系统量子力学不稳定。自伴性和重整化技术通常提供系统一个标度，从而使基态从下有界。另一方面，我们使用非对易量子力学，并利用非对易参数Θ作为标度对称系统的标度。由此产生的系统的哈密顿量，然后允许一个不寻常的束缚态在阈值的能量，E=0。除了哈密顿量\hat{H}外，我们还计算了so（2，1）代数的另外两个生成元：膨胀\hat{D}和保形生成元\hat{K}. so（2，1）代数在非对易空间中不是封闭的，但极限Θ \to 0平滑地到达恢复共形对称的so（2，1）代数.我们还讨论了大非对易参数的系统。
英文摘要：
The ground state energy of a scale symmetric system usually does not possess any lower bound, thus making the system quantum mechanically unstable. Self-adjointness and renormalization techniques usually provide the system a scale and thus making the ground state bounded from below. We on the other hand use noncommutative quantum mechanics and exploit the noncommutative parameter Θas a scale for a scale symmetric system. The resulting Hamiltonian for the system then allows an unusual bound state at the threshold of the energy, E=0. Apart from the Hamiltonian \hat{H} we also compute the other two generators of the so(2,1) algebra, the dilation \hat{D} and the conformal generator \hat{K} in the noncommutative space. The so(2,1) algebra is not closed in the noncommutative space, but the limit Θ\to 0 smoothly goes to the so(2,1) algebra restoring the conformal symmetry. We also discuss the system for large noncommutative parameter.
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