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Charge Conjugation and Internal Symmetry Representations
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Feb12-12, 08:25 PM
I am trying to work through a QFT problem for independent study and I can't quite get my head around it. It is 5.16 from Tom Bank's book (http://www.nucleares.unam.mx/~alberto/apuntes/banks.pdf) which goes as follows:
"Show that charge conjugation symmetry implies that the representation of the internal symmetry group G is real or pseudo-real." (I think we only need to deal with scalar fields here but I don't know that it matters.)
The book linked to above has more details on pages 50-52. I am am pretty confused but I think that I need to show that the representation [itex]R_S[/itex] is not complex if C-symmetry exists. That is to show that [itex]R_s^\dagger=U^\dagger R_s U[/itex]. (i.e. unitary equivalence) is implied by C-symmetry on scalar fields.
Thanks in advance for any help.
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