The definition of tensor operator that I have is the following: 'A tensor operator is an operator that transforms under an irreducible representation of a group ##G##. Let ##\rho(g)## be a representation on the vector space under consideration then ##T_{m_c}^{c}## is a tensor operator in the irreducible representation ##c## if it transforms as follows: $$\rho(g) T_{m_c}^c \rho(g)^{\dagger} = (\rho_c(g))_{m_c m'_c} T_{m_c'}^c,$$ with summation over ##m_c'## implied.(adsbygoogle = window.adsbygoogle || []).push({});

Can someone give me an example of a tensor operator realized in physics and the motivation for such a definition?

Also, in that definition, what does it mean to say '...an operator that transforms under an irreducible representation of a group.'

Thanks.

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# Understanding tensor operators

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