$κ$ -Minkowski时空与DSR代数：新面貌与老问题
$κ$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
摘要：
在霍普夫代数公式中重新考虑了变形狭义相对论（DSR）中的某些理论.为此目的，我们将探讨变形Weyl-Heisenberg代数的最小框架提供了一个粉碎的产品建设DSR代数。证明了这种唯一统一了$κ$ -Minkowski时空坐标和Poincaré生成元的DSR代数可以由未变形的生成元通过非线性变换得到。它在标准（未变形）Weyl-Heisenberg代数中的各种实现为相对论（Stückelberg版本）量子力学中DSR理论的量子力学解释开辟了道路。在此基础上，我们回顾了最近的一些结果，扭曲实现的$κ$ -Minkowski时空描述为一个量子协变代数决定了相应的线性泊松结构的变形量子化。讨论了量子$κ$ -Poincaré和$κ$ -Minkowski代数以及DSR理论的形式和概念问题。特别是，所谓的“$q$ -模拟”版本的DSR代数的介绍。双狭义相对论的量子化仍然是一个悬而未决的问题。最后，可能的物理应用DSR代数的普朗克尺度物理的某些方面的描述简要回顾。
英文摘要：
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies $κ$-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed) Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version) Quantum Mechanics. On this basis we review some recent results concerning twist realization of $κ$-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum $κ$-Poincaré and $κ$-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called "$q$-analog" version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
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