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Why internal symmetry is always compact and semisimple Lie group up to U(1)?

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Why internal symmetry is always compact and semisimple Lie group up to U(1)? Is there internal symmetry non-compact or non-semisimple?

closed as a duplicate of: Why is the Yang-Mills gauge group assumed compact and semi-simple?

asked Jan 19, 2015 in Closed Questions by Alienware (185 points) [ no revision ]
recategorized Jun 22, 2015 by dimension10

Basically in order to have a positive-definite kinetic term in the Lagrangian, see this post. If you are happy with the answer therein I propose to close the question as duplicate.

commented Jan 19, 2015 by Jia Yiyang (2,640 points) [ no revision ]
edited Jan 19, 2015 by Jia Yiyang

The complete answer is given by Stan in the post linked to by Jia Yiyang.

commented Mar 3, 2015 by Arnold Neumaier (15,787 points) [ no revision ]

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