Correlation (Green's) Functions and the Functional Derivative

W. E. Parry, Roy E. Turner

Thermodynamic perturbation theory is described in terms of temperature-dependent Green functions. The relationship of these functions with time-temperature-dependent Green functions and with correlation functions is discussed and some of their analytic properties are derived. The chain of coupled equations forming the equations of motion of the Green functions is derived and is written in terms of functional derivatives. Two examples of the use of Green functions, discussions of the sharpness of the Fermi surface and of neutron scattering from liquid helium, are given. The use of Green functions in the theory of relaxation phenomena is described.

Peter Millington

Andrij M. Shvaika

A general approach to the derivation of the spectral relations for the multitime correlation functions is presented.A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions.Representation of the multitime Green functions in terms of the spectral densities and solution of the reverse problem, i.e., finding the spectral densities from the known Green functions, are given for the case of the three-time correlation functions.

Ulrich Hohenester

Zuo Wei, Hua Guo, Shun-Jin Wang

With the aid of generating-functional technique, the many-body correlation dynamics was generalized to the relativistic cases within a Green's function formalism and two sets of equations of motion for the correlation (or connected) Green's functions were derived respectively for the scalar -model and the Yukawa model, which were nonperturbative in nature and could provide physically transparent truncations with respect to the order of correlations.

Jurgen Michael Honig, Józef Spałek