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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?
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.

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

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