To expand Green's function (G), we have two solutions depending on whether r>r' or r'>r to avoid divergence. On the contrary, it has been argued [1] that the imaginary part of Green's function (Im G) is regular everywhere and hence can be expanded in regular waves.
I wonder why is (Im G) regular and how to arrive at eq (82) in Ref. 1 from eq (81)? Also, why (Im G) is expanded only on propagating waves?
Is the real part of Green's function (Re G) also regular?
[1] Krüger, Matthias, et al. "Trace formulas for nonequilibrium Casimir interactions, heat radiation, and heat transfer for arbitrary objects." Physical Review B 86.11 (2012): 115423.
Dear Mohamed Ismail Abdelrahman
I am not familiar with the term regular Green function. But I am familiar with the formalism for solid-state:
The imaginary part of the green function allows calculating the expectation values of operators and it is very important to understand its math properties.
The properties of the Imag [G(omega)] depend on whether omega is >0 or
Dear P. Contreras
Thank you very much for your answer, I really appreciate that.
You are welcome, Dear Mohamed Ismail Abdelrahman
Is one of the hardest questions, I have found on RG, Best Regards.
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