Retarded and Advanced Green Functions in Statistical Physics

J. G. G. S. Ramos, A.A. Gomés

N. N. Bogolyubov, Sergei Vladimirovich Tyablikov

An approximation method is outlined for resolving problems in statistical physics, based on the analysis of Green's two-dimensional retarded and advanced functions, with the application of the Lehmann-Callen spectral representation. (R.V.J.) with alternating conductance, when the magnetic field rises in transition through the shock wave. (R.V.J.)

Norman J. M. Horing

Abstract Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

D. ter Haar

В. Л. Бонч-Бруевич, Sergei Vladimirovich Tyablikov, Raymond J. Seeger

P C Kwok, T D Schultz

The zero-frequency anomaly that can arise in the Fourier transform of certain quantum mechanical correlation functions is investigated. Two physical interpretations are given to the anomalous term. It is shown that any method for calculating the thermal Green function (though not the retarded or advanced commutator Green functions) should also yield the strength of the anomaly. An example is given. A critical discussion is given of recent contributions by other authors.