论文标题
长度最小的空间和时间变换
Space and time transformations with a minimal length
论文作者
论文摘要
量子重力的现象学研究提出了对量子力学中位置和动量之间换向因子的修改，以便在量子力学中引入最小的不确定性。这种最小的不确定性和随之而来的最小可测量长度对量子系统的动力学有重要影响。在目前的工作中，我们表明，这种后果超越了动态，达到了能量，动量和同一哈密顿量等数量的定义。此外，由于哈密顿量定义为时间演变的发生器，因此将被界限，所以最小的长度意味着最小的时间。
Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty and the consequent minimal measurable length have important consequences on the dynamics of quantum systems. In the present work, we show that such consequences go beyond dynamics, reaching the definition of quantities such as energy, momentum, and the same Hamiltonian. Furthermore, since the Hamiltonian, defined as the generator of time evolution, results to be bounded, a minimal length implies a minimal time.
