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Up to now, I've been not so familiar with theoretical condensed matter physics but now I have to calculate a partition function of the type

[tex]Z = \mathrm{Tr}\,\mathrm{e}^{-\beta(a^\dagger a + a^\dagger b + ab^\dagger)}[/tex]

where [itex]a, a^\dagger, b, b^\dagger[/itex] arefermionicannihilition/creation operators. I want to take only a partial trace over the [itex]a[/itex]-particles. I've tried several things such as BHC and the Trotter product formula and evaluation of the exponential for certain parts of the Hamiltonian but I've obtained nothing which is actually feasible. I've had a look in several books about many-particle quantum theory but found nothing useful. Is this problem elementary? Any ideas or literature recommendations?

Thanks!!

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# Fock space tracing techniques

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