论文标题
$ p^{4} $的自动偶会扩展在有限的间隔上校正的粒子的哈密顿量
Self-adjoint extensions for a $p^{4}$-corrected Hamiltonian of a particle on a finite interval
论文作者
论文摘要
在本文中，我们讨论了找到$ p^4 $校正的哈密顿式的自我伴侣扩展的问题。该主题的重要性在于量子力学的概念在最小长度的场景中的应用，该量表描述了量子重力的有效理论。我们在有限的一维间隔中工作，并给出导致自动化扩展的显式$ u（4）$参数化。一旦知道参数化，我们就可以选择适当的$ U（4）$矩阵来建模物理问题。作为示例，我们讨论了无限的方孔，周期性条件，抗周期条件和周期性条件，直到处方阶段。我们希望我们发现的参数化将有助于在进一步的工作中建模其他有趣的物理情况。
In the present paper we deal with the issue of finding the self-adjoint extensions of a $p^4$-corrected Hamiltonian. The importance of this subject lies on the application of the concepts of quantum mechanics to the minimal-length scale scenario which describes an effective theory of quantum gravity. We work in a finite one dimensional interval and we give the explicit $U(4)$ parametrization that leads to the self-adjoint extensions. Once the parametrization is known, we can choose appropriate $U(4)$ matrices to model physical problems. As examples, we discuss the infinite square-well, periodic conditions, anti-periodic conditions and periodic conditions up to a prescribed phase. We hope that the parametrization we found will contribute to model other interesting physical situations in further works.
