Obtaining a unitary representation for a given group.nb (63.5 KB)
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Nice. Thanks for sharing. BTW, one useful built-in function: UnitaryMatrixQ
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Very nice. I have a question though. You create a new matrix by summing the generators and orthogonalize this new one. How do you know the transform will then simultaneously orthogonalize each summand? Does this come from the theory?
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This works because they commute
Table[gT[[i]] . gT[[j]] == gT[[j]] . gT[[i]], {i, 4}, {j, i, 4}]
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Hello Dan. Strictly spoken I sum not over generators, but over the whole group. That is the trick that
Conjugate[T[a]] . H . T[a] equals H.
The details are outlined in the text cited.
Correction: it must be of course
TransposeConjugate[T[a]] . H . T[a] equals H.
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