The 'partition function' in QFT is written as [itex]Z=\langle 0 | e^{-i\hat H T} |0\rangle[/itex], but I'm having a difficult time really understanding this. I'm assuming that [itex]|0\rangle[/itex] represents the vacuum state with no particles present. If that's the case, and the Hamiltonian acting on such a state would just produce the ground state energy, which can be defined to be zero. How does this give you anything interesting then? If [itex] e^{-i\hat H T} |0\rangle=e^{-i (0)T}|0\rangle[/itex], then I fail to see how this quantity is of any use. (I know that by adding a source to the Hamiltonian, you can calculate the interaction energy of two particles, but for a source free H I'm not sure what it does). Also, if you have a Hamiltonian of the form [itex]:\hat H:=\sum_{k}\hat a^{\dagger}_{k}\hat a_{k}[/itex], where [itex]\hat a_{k}|0\rangle=0[/itex], then I really don't get what's going on here when you write out Z. Does it only make sense to calculate this when you have a source term added?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks in advance for any help

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# Field Theory Partition Function

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