Hermiticity of the Dirac Hamiltonian in curved spacetime
Hermiticity of the Dirac Hamiltonian in curved spacetime
复制标题
弯曲时空中狄拉克哈密顿量的厄米性
DOI：
10.1103/physrevd.79.024020
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
L. Parker
中科院分区：
文献类型：
--
作者：
Xing Huang;L. Parker
在以前关于原子在一般弯曲背景时空中自由下落的量子力学的研究中，度规被认为在与原子跃迁相关的时间尺度上变化足够缓慢，以至于原子附近度规的时间导数可以忽略不计。然而，当度量的时间依赖性不能被忽略时，它表明那里使用的哈密顿量对于守恒标积不是埃尔米特的。这个哈密顿量直接从弯曲时空中的狄拉克方程得到。这就产生了一个悖论，即这个哈密顿量怎么可能是非厄米的。在这里，我们表明，这种非厄米性的结果从时间依赖性的位置本征态进入薛定谔波函数，我们写的表达式是厄米的一般度量时，度量的时间依赖性不被忽略的哈密顿量。
In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-Hermitian. Here, we show that this non-Hermiticity results from a time dependence of the position eigenstates that enter into the Schroedinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time dependence of the metric is not neglected.