Electrodynamics and Spacetime Geometry: Foundations

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• 作者：Francisco Cabral ; Francisco S. N. Lobo
• 关键词：Electrodynamics ; (pseudo) ; Riemann geometry ; Constitutive relations
• 刊名：Foundations of Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：47
• 期：2
• 页码：208-228
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：History and Philosophical Foundations of Physics; Quantum Physics; Classical and Quantum Gravitation, Relativity Theory; Statistical Physics and Dynamical Systems; Classical Mechanics; Philosophy of S
• 出版者：Springer US
• ISSN：1572-9516
• 卷排序：47

文摘

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.