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- Thread starter mma
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Ben Niehoff

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This assumes that your vector transforms in the fundamental representation. The same procedure applies to any representation, though. Simply write out the most generic quadratic form, and see which terms remain invariant under the action of the group. For example, the symmetric, traceless tensor rep will have 5-tuples of numbers, and hence 25 terms in its quadratic form.

You can take a shortcut and note that the quadratic form must be diagonal, since SO(3)-invariance implies space is isotropic.

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Hurkyl

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Ben Niehoff

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Yes. Isn't that what the OP was asking?

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