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atyy

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http://www.colorado.edu/physics/phys7240/phys7240_fa14/notes/Week8.pdf

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You cannot introduce even a definition of normal ordering without a mode decomposition of a field in terms of annihilation and creation operators with respect to some single-particle basis. Such a decomposition only exists for free fields and that's why one uses the interaction picture.

In addition, it's important to note that Wick's theorem is valid if and only if the initial state is given by a statistical operator of the form ##\hat{\rho}=\exp(-\hat{A})##, where ##\hat{A}## is an appropriate single-particle operator. The special case of vacuum QFT, i.e., when ##\hat{\rho}=|\Omega \rangle \langle \Omega |## can be taken as the zero-temperature limit and zero-chemical potential(s) limit of the grand-canonical ensemble, ##\hat{\rho}=\exp(-\beta \hat{H})/Z## with ##Z=\mathrm{Tr} \exp(-\beta{\hat{H}})##, ##\beta=1/(k_B T)##.

For a very good introduction on these issues, see

Danielewicz, P.: Quantum Theory of Nonequilibrium Processes II. Application to Nuclear Collisions, Ann. Phys.**152**, 305–326, 1984

http://dx.doi.org/10.1016/0003-4916(84)90093-9 [Broken]

In addition, it's important to note that Wick's theorem is valid if and only if the initial state is given by a statistical operator of the form ##\hat{\rho}=\exp(-\hat{A})##, where ##\hat{A}## is an appropriate single-particle operator. The special case of vacuum QFT, i.e., when ##\hat{\rho}=|\Omega \rangle \langle \Omega |## can be taken as the zero-temperature limit and zero-chemical potential(s) limit of the grand-canonical ensemble, ##\hat{\rho}=\exp(-\beta \hat{H})/Z## with ##Z=\mathrm{Tr} \exp(-\beta{\hat{H}})##, ##\beta=1/(k_B T)##.

For a very good introduction on these issues, see

Danielewicz, P.: Quantum Theory of Nonequilibrium Processes II. Application to Nuclear Collisions, Ann. Phys.

http://dx.doi.org/10.1016/0003-4916(84)90093-9 [Broken]

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Thank you, that puts me on the trail.

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