关于狭义相对论的Snyder-Sidharth变形的某些结果
On some consequences of the Snyder-Sidharth deformation of Special Relativity
摘要：
宇宙中存在最小尺度的假设导致了时空的非对易几何，从而导致了对狭义相对论约束的修正。Sidharth已经推断出这等价于洛伦兹对称性破坏。后一种考虑也被科汉豪、科尔曼和其他学者使用，尽管他们是基于超高能宇宙射线和伽玛暴的观测所提出的纯现象学模型。另一方面，包括Sidharth在内的一些作者提出了一个小但非零的光子质量$m_γ>0$的建议，这种质量在实验允许的范围内。这也导致了在极高能量的伽马射线中原则上可观察到的洛仑兹对称性的微小破坏，正如事实上所声称的那样。本文研究了Snyder-Sidharth哈密顿量，并对Dirac-Sidharth哈密顿量作了简要的评述，它是对可观测到的Lorentz对称性破坏的一种可能的解释。
英文摘要：
The hypothesis on a minimal scale existence in the Universe leads to noncommutative geometry of Spacetime and thence to a modification of the Special Relativity constraint. Sidharth has deduced that this is equivalent to the Lorentz symmetry violation. This latter consideration was also used by Glashow, Coleman and other scholars though based on purely phenomenological models that have been suggested by the observation of Ultra High Energy Cosmic Rays and Gamma Bursts. On the other hand a parallel development has been the proposal of a small but nonzero photon mass $m_γ>0$ by some authors including Sidharth, such a mass being within experimentally allowable limits. This too leads to a small violation of the Lorentz symmetry observable in principle in very high energy gamma rays, as in fact is claimed. In this paper we study the Snyder--Sidharth Hamiltonian and briefly comment the Dirac--Sidharth Hamiltonian, that is a possible explanation for observable violation of the Lorentz symmetry.
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