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arXiv · hep-th/0210214

Yang-Mills theory for non-semisimple groups

Jean Nuyts·Tai Tsun Wu
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Abstract

For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail.

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Jean Nuyts, Tai Tsun Wu. 2002-10-22. Yang-Mills theory for non-semisimple groups. https://doi.org/10.1103/physrevd.67.025014

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