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In page 86, in Peskin & Schroeders Introduction to QFT, the following expression is introduced to analyze [tex] \left | \Omega \right >; [/tex] the ground state of the interacting theory:

[tex] e^{-iHT} \left | 0 \right >. [/tex]

Where |0> is the ground state of the free theory and H is the Hamiltonian of the interacting theory. What is this expression? It is not the dirac picture free theory ground state, and it can't be just a time translation of the free theory ground state. Well maybe it is but I never saw this in my QM days.

Furthermore, the expression is equated to

[tex] e^{-iHT} \left | 0 \right > = \Sigma_n e^{-iE_nT} \left | n \right > \left < n \right | 0 >. [/tex]

Don't |n> and |0> belong to different Hilbert spaces? Am I missing something here?

Thanks for any clarification!

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# Peskin page 86

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