It seems that according to the formula, when the eigenvalues of one of the matrices inside the trace of the IZ integral are degenerate, the integral diverges.(adsbygoogle = window.adsbygoogle || []).push({});

Is it correct or the formula is different for this case? For instance, suppose the group is U(N) and I want to calculate

[tex]\int dU \, \exp\left[\mbox{Tr} (U A U^\dagger \sigma^1_z)\right][/tex]

whereAis Hermitean and [tex]\sigma^1_z[/tex] is the spin in the Z direction of the first spin in a 2-qubit system, i.e., the direct product of two Z Pauli matrices. Is the integral divergent in this case?

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# Itzykson-Zuber Integral & Degenerate Eigenvalues

Can you offer guidance or do you also need help?

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