Maxwell’s equations for free fields are studied on the underlying C∞ manifold of a compact Lie group. The formulation is in terms of exterior differential forms as given by Wheeler. It is found that on a compact connected Lie group there are no free electromagnetic fields. The results obtained are essentially a physical interpretation of the well‐known theorem that the second Betti number of a compact semisimple Lie group is zero.
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S. Goldberg, Curvature and Homology (Academic, New York, (1962).
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P. M. Cohn, Lie Groups (Cambridge U.P., Cambridge, (1957).
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© 1977 American Institute of Physics.
1977
American Institute of Physics
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