Undergrad What Causes Ambiguity in Wick Rotation for Time-Ordered Correlators?

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The discussion centers on the confusion surrounding the Wick rotation for time-ordered correlators, particularly the distinction between cases when time is greater than or less than zero. The accepted answer in the referenced post highlights the role of the factor ##e^{\pm i\pi}##, which arises from the negative sign in front of ##t^{2}##. Participants express uncertainty about the source of ambiguity in the final results of the correlators. The conversation emphasizes the importance of understanding the implications of time ordering in quantum field theory. Clarifying these points is essential for grasping the nuances of Wick rotation in this context.
thatboi
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Hi all,
I am reading the following post: https://physics.stackexchange.com/q...o-time-ordered-correlator-in-real-time-how-do
and was confused regarding the portion in the accepted answer where they made a distinction for the ##t>0## and ##t<0## case. I believe the ##e^{\pm i\pi}## factor comes from the negative sign in front of ##t^{2}## but cannot understand why there is an ambiguity in the final result.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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