论文标题
Schrodinger-Newton模型的相对论概括，以减少波功能
Relativistic generalization of the Schrodinger-Newton model for the wavefunction reduction
论文作者
论文摘要
我们考虑了L. diosi，R。Penrose等人提出的自我驱动的自发波函数还原的模型。并基于Schrodinger和Poisson方程的自洽系统。提出了一个相似的狄拉克和麦克斯韦方程的类似系统作为相对化。后者的常规解决方案形成一个离散的频谱，其中所有“主动”重力质量始终为正，并且大约等于惯性质量和dirac场量子的质量$ m $，直到校正$α^2 $。这里$α=（m/m_ {pl}）^2 $是细胞核的良好结构常数的重力模拟。在限制$α\至0 $的情况下，该模型还原回了非士兵的施罗丁格 - 纽顿。等效原则以极高的精度实现。上述溶液对应于相同（游离）粒子的各种状态，而不是不同的粒子。这些状态在特征上的差异很小，但在波形的宽度上基本上有所不同。对于基态，后者是$α$乘以康普顿长度的倍，因此核子不能充分定位以建模还原过程
We consider the model of the self-gravity driven spontaneous wavefunction reduction proposed by L. Diosi, R. Penrose et al. and based on a self-consistent system of the Schrodinger and Poisson equations. An analogous system of coupled Dirac and Maxwell-like equations is proposed as a relativization. Regular solutions to the latter form a discrete spectrum in which all the "active" gravitational masses are always positive, and approximately equal to inertial masses and to the mass $m$ of the quanta of Dirac field up to the corrections of order $α^2$. Here $α=(m/M_{pl})^2$ is the gravitational analogue of the fine structure constant negligibly small for nucleons. In the limit $α\to 0$ the model reduces back to the nonrelativistic Schrodinger-Newton one. The equivalence principle is fulfilled with an extremely high precision. The above solutions correspond to various states of the same (free) particle rather than to different particles. These states possess a negligibly small difference in characteristics but essentially differ in the widths of the wavefunctions. For the ground state the latter is $α$ times larger the Compton length, so that a nucleon cannot be sufficiently localized to model the reduction process
