Some Useful Operators on Differential Forms on Galilean and Carrollian Spacetimes

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2022-06-22 DOI:10.3842/SIGMA.2023.024

M. Fecko

引用次数: 1

Abstract

Differential forms on Lorentzian spacetimes is a well-established subject. On Galilean and Carrollian spacetimes it does not seem to be quite so. This may be due to the absence of Hodge star operator. There are, however, potentially useful analogs of Hodge star operator also on the last two spacetimes, namely intertwining operators between corresponding representations on forms. Their use could perhaps make differential forms as attractive tool for physics on Galilean and Carrollian spacetimes as forms on Lorentzian spacetimes definitely proved to be.

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关于Galilean和Carrollian时空微分形式的一些有用算子

洛伦兹时空的微分形式是一个公认的课题。在伽利略和卡罗利亚的时空中，情况似乎并不完全如此。这可能是由于霍奇星操作员的缺席。然而，在最后两个时空上，也有可能有用的霍奇星算子的类似物，即形式上相应表示之间的交织算子。它们的使用可能会使微分形式成为伽利略和卡罗利时空物理学的一种有吸引力的工具，就像洛伦兹时空的形式一样。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.