A topological theory of the electromagnetic field
A topological theory of the electromagnetic field
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DOI：
10.1007/bf00401864
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发表时间：
1989-08
影响因子：
1.2
通讯作者：
A. Rañada
中科院分区：
文献类型：
--
作者：
A. Rañada
结果表明，真空中的麦克斯韦方程源自由标量场 phi 给出的基础拓扑结构，该标量场表示映射 S3×R→S2，并通过一定的变换确定电磁场，这也将高度非线性场方程线性化为麦克斯韦方程。因此，真空中的麦克斯韦方程具有拓扑解，其特征在于霍普夫指数等于任何一对磁力线的链接数。这允许将电磁场分类为同伦类，并由螺旋度值标记。尽管模型仅使用c数域，但螺旋性总是验证∫A·Bd3r=nα，n是整数，α是作用常数，由于维数原因，这必然出现在理论中。
It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field ϕ which represents a mapS3×R→S2and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of onlyc-number fields, the helicity always verifies ∫A·Bd3r=nα,nbeing an integer and α an action constant, which necessarily appears in the theory, because of reasons of dimensionality.