Search for combinations of thermaln-point functions with analytic extensions

Abstract

The 2 n different n-point functions that occur in real-time thermal field theory are Fourier transformed to real energies. Because of branch cuts in various energy variables, none of these functions can be extended analytically to complex energies. The known linear combinations that form the fully retarded and advanced functions can be extended analytically. It is proven that no other linear combinations have an analytic extension to complex energies.

Multipoint correlation functions: spectral representation and numerical evaluation

“…This is the analytic continuation between MF p functions and (fully) retarded ones in the KF [24,43,44]. It generalizes the well known 2p relation G 21/12 (ω) = G(iω → ω ± ).…”

“…In the most complex setup of the KF with Keldysh basis, where each argument has an extra Keldysh index 1 or 2, we find that those components with a single Keldysh index equal 2 at position η, dubbed G [η] , have the simplest structure. Indeed, they are the (fully) retarded objects which can be obtained from Matsubara p functions via a suitable analytic continuation, iω i → ω i ± i0 + [24]. This does not apply to the remaining Keldysh components.…”

“…The sequence [µ 1 ... µ α ] lists the new slots of the 2's; placing its elements in increasing order yields [η 1 ... ηα ]. For example, if k = 1212 = [24], then p = (4123) yields [µ 1 µ 2 ] = [31] and k p = 2121 = [13].…”