标题： 森古普塔变换与卡罗来亚相对论理论 显示英文标题

标题： Sengupta Transformations and Carrollian Relativistic Theory

摘要： 给出了卡罗尔相对论的详细且系统的表述。基于森古普塔[19]首先提供的变换，我们构建了洛伦兹相对论矢量和卡罗尔相对论矢量之间的映射。利用这个映射，从标准的麦克斯韦作用量构建了卡罗尔理论。我们证明可以从作用量中得到自洽的运动方程，无论是在电极限还是磁极限下。我们引入了卡罗尔电场和磁场。推导出了一组新的映射，这些映射将卡罗尔电场和磁场与通常的麦克斯韦场联系起来，并以场的形式给出卡罗尔方程。结果与势表述的一致性得到了验证。详细讨论了像对偶性、规范性、位移、诺特定理和速度增强等卡罗尔对称性的版本，并对其含义进行了阐述。特别是，速度增强对称性提供了一个与本文中使用的各种映射的联系。 显示英文摘要

摘要： A detailed and systematic formulation of Carrollian relativity is provided. Based on the transformations, first provided by Sengupta [19], we construct a mapping between Lorentz relativistic and Carrollian relativistic vectors. Using this map the Carroll theory is built from the standard Maxwell action. We show that we get self-consistent equations of motion from the action, both in electric and magnetic limits. We introduce Carroll electric and magnetic fields. A new set of maps is derived that connects Carroll electric and magnetic fields with the usual Maxwell ones and yields Carroll equations in terms of fields. Consistency of results with the potential formulation is shown. Carroll version of symmetries like duality, gauge, shift, Noether and boost are treated in details and their implications elaborated. Especially, boost symmetry provides a link to the various maps used in this paper.