论文标题
无限维代数作为运动代数的扩展
Infinite-dimensional algebras as extensions of kinematic algebras
论文作者
论文摘要
运动代数可以在几何空间上实现，并约束可以在这些空间上生活的物理模型。存在不同类型的运动代数，我们将这些代数的相互作用考虑相对论系统的非偏见限制的相互作用，包括Galilei和Carroll限制。我们开发了一个框架，该框架通过引入新的无限维代数来系统地捕获严格的非相关限制，重点是卡罗尔案。我们的结果之一是强调加里利和卡洛尔限制之间的一种新型二元性，该二元性也扩展到校正。我们在粒子模型方面意识到这些代数。其他应用包括背景电磁场中的曲率校正和颗粒。
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits of a relativistic system, including both the Galilei and the Carroll limit. We develop a framework that captures systematically the corrections to the strict non-relativistic limit by introducing new infinite-dimensional algebras, with emphasis on the Carroll case. One of our results is to highlight a new type of duality between Galilei and Carroll limits that extends to corrections as well. We realise these algebras in terms of particle models. Other applications include curvature corrections and particles in a background electro-magnetic field.
