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<p>This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell’s equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a <i>p</i>-form in an <i>n</i>-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="161_2025_1364_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="82" /> </InlineMediaObject> <EquationSource Format="TEX">\((n-p-1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mi>p</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-form, a generalization of the Maxwell 2-form.</p>

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Electrodynamics and geometric continuum mechanics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月17日

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  • Reuven Segev

摘要

This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple generalization of the fields of electrodynamics and Maxwell’s equations to general differentiable manifolds of any dimension, thus viewing generalized electrodynamics as a special case of continuum mechanics. The basic kinematic variable is the potential, which is represented as a p-form in an n-dimensional spacetime. The stress for the case of generalized electrodynamics is assumed to be represented by an \((n-p-1)\) ( n - p - 1 ) -form, a generalization of the Maxwell 2-form.