伽利略和卡罗尔霍奇星算子

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-02-01 DOI:10.1016/S0034-4877(24)00007-7

Marián Fecko

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引用次数: 0

摘要

标准霍奇星算子与度量张量（和方向）天然相关。它通常用于简明地写出洛伦兹时空的物理方程。而在伽利略（卡罗尔）时空，则没有正则（非ingular）度量张量可用。因此，通常的霍奇星构造不起作用。在这里，我们提出了伽利略（卡罗尔）时空的霍奇星算子的类似物。它们可以用来写出重要的物理方程，例如伽利略（卡罗尔）电动力学方程。

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Galilean and Carrollian Hodge star operators

The standard Hodge star operator is naturally associated with metric tensor (and orientation). It is routinely used to concisely write down physics equations on, say, Lorentzian spacetimes. On Galilean (Carrollian) spacetimes, there is no canonical (nonsingular) metric tensor available. So, the usual construction of the Hodge star does not work. Here we propose analogs of the Hodge star operator on Galilean (Carrollian) spacetimes. They may be used to write down important physics equations, e.g. equations of Galilean (Carrollian) electrodynamics.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.