标题： 森古普塔变换和卡罗尔ian相对论理论 显示英文标题

标题： Sengupta Transformations and Carrollian Relativistic Theory

摘要： 提供了Carroll相对论的详细和系统表述。 基于Sengupta [18]首先提供的变换，我们构建了洛伦兹相对论和Carroll相对论矢量之间的映射。 使用这个映射，从标准麦克斯韦作用量构建了Carroll理论。 我们证明了从作用量中可以得到自洽的运动方程，包括电极限和磁极限情况。 我们引入了Carroll电场和磁场。 推导出一组新的映射，将Carroll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Carroll方程。 展示了结果与势表述的一致性。 详细处理了如对偶性、规范、位移、诺特和提升等对称性的Carroll版本，并阐述了它们的含义。 特别是，提升对称性提供了与本文中使用的各种映射之间的联系。 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 [18], 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.