The discussion focuses on the application of the time ordering operator in the context of imaginary time formalism, specifically regarding the derivation of Green's functions. The key equations referenced are 10.15 and 10.16 from the text "Many-body quantum theory in condensed matter physics" by Henrik Bruus and Karsten Flensberg. It is established that under time ordering, all U(τ) terms can be collected and subsequently canceled, which is crucial for understanding the transition between the two equations. The time ordering operator's behavior is clarified, indicating that it has no effect when τ > τ' and reverses the order when τ' > τ.
PREREQUISITESStudents and researchers in theoretical physics, particularly those focusing on quantum mechanics and many-body systems, will benefit from this discussion. It is especially relevant for those looking to deepen their understanding of imaginary time formalism and Green's functions.