论文标题
三维高阶Schrödinger代数和谎言代数扩展
Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions
论文作者
论文摘要
我们提供了一个谎言代数扩展程序，以构建三维高阶Schrödinger代数，该代数依赖于四维相对论形式的共同代数的特定亚代代数。特别是，我们重现了扩展的Schrödinger代数，并提供了新的高阶Schrödinger代数。该新代数的结构导致讨论高阶非相关代数的独特性。尤其是，我们表明，牛顿重力的动作原理的最近的D维对称代数不是唯一定义的，而是可以容纳三个离散参数。对于这些参数的特定选择，Bargmann代数成为该扩展代数的子代数，该代数使人们可以在Bargmann-Invariant Sense中引入质量电流，从而向扩展理论引入。
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrödinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrödinger algebra and provide a new higher-order Schrödinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.
