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Why does a theory described by a non-abelian group has only a single coupling constant $g$? While on the other hand in an abelian theory, as Electromagnetism, each charged particle has its own charge with which its interacts with the gauge fields?

In Grand Unified Theory by P. Langacker, its is mentioned it the beginning of section III that model described by a group $$G= G_1\times \cdots \times G_1 \times D ,$$ where $D$ a discrete subgroup that permutes identical factors $G_1$, is also described by a single coupling constant. Why?

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Comments to the question (v2):

  1. For a reductive Lie group of the form $G=G_1\times \ldots \times G_n$, where each factor $G_i$ is either simple or $U(1)$, then there exists an independent coupling constant $g_i$ for each factor $G_i$. In particular, a non-abelian Lie group can have more than one coupling constant.

  2. The article Grand Unified Theory by P. Langacker is talking about the case where a discrete subgroup $D$ permutes identical factors $G_1$. Then there is no room for individual coupling constants, only a single common coupling constant for all $G_1$-copies.

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