I am wondering why, e.g., the book by Mahan, "Many-particle physics", mentions that contractions in Wick theorem for the $N$-particle Matsubara Green function between a pair of operators at equal times must be computed by putting the creation operator to the left of the annihilation one. Where does this rule come from? Why is it correct, if time-ordering is not well defined for equal times?
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Possible duplicates: https://physics.stackexchange.com/q/133426/2451 and links therein. – Qmechanic Feb 01 '23 at 00:37
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@Qmechanic this is not a duplicate with the link you mention. The need for some care at equal times lies within the nature of the definition of the imaginary-time Green-function (or the Matsubara-GF respectively): In the definition you make explicit use of theta-functions. However... You will notice that in practice this won't be bothering you too much since you basically never work with these theta-functions when you are computing self-energies. The rule that you mention is imho just some convention to satisfy the pedants. – Antihero Jun 17 '23 at 23:21
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General tip: Editing a post automatically propels it to the review queue. – Qmechanic Jun 18 '23 at 03:55