标题： 超越自旋：无自旋量子力学中的扭折驱动非线性 显示英文标题

标题： Beyond Spin: Torsion-Driven Nonlinearity in Spinless Quantum Mechanics

摘要： 我们研究了非相对论、无自旋粒子在具有挠率的弯曲空间中传播的以前未被探索的量子动力学。 我们的发现表明，虽然挠率主要与自旋相关，但它也可以通过量子涨动在薛定谔方程中引入对数非线性，从而影响无自旋粒子的量子行为，即使是在平坦的空间中也是如此。 为了便于在弯曲空间中进行量子化，我们引入了一种新的随机变分方法。 与正则量子化不同，这种方法自然适用于广义坐标系统，量子涨落来源于随机过程中一个直接受挠率影响的噪声项。 通过要求与量子动力学的一致性，我们最终推导出了挠率大小的一个上限。 我们的结果揭示了一个以前未被认识的机制，即挠率（如在广义相对论某些扩展理论中所预测的）可以影响量子系统的方式，这可能对早期宇宙物理学以及暗物质或能量模型产生潜在影响。 显示英文摘要

摘要： We investigate the previously unexplored quantum dynamics of non-relativistic, spinless particles propagating in curved spaces with torsion. Our findings demonstrate that while torsion has been predominantly associated with spin, it can also influence the quantum behavior of spinless particles by inducing a logarithmic nonlinearity in the Schroedinger equation through quantum fluctuations, even in flat space. To facilitate quantization in curved spaces, we introduce a novel stochastic variational method. Unlike canonical quantization, this approach is naturally suited to general coordinate systems, with quantum fluctuations arising from a noise term in the stochastic process that is directly influenced by torsion. By requiring consistency with quantum dynamics, we ultimately derive an upper bound on the magnitude of torsion. Our results reveal a previously unrecognized mechanism by which torsion, as predicted in certain extensions of general relativity, can influence quantum systems, with potential implications for early-universe physics and dark matter or energy models.