Functional techniques in physics

Nguyễn Văn Hiếu

A. B. Balantekin

E. Gozzi

Huai‐Yu Wang

Part I: Green's Functions in Mathematical Physics - Time-Independent Green's Functions / Time-dependent Green's Functions / Part II: One-Body Green's Functions - Physical Significance of One-Body Green's Functions / Green's Functions and Perturbation Theory / Green's Functions for Tight-Binding Hamiltonians / Single Impurity Scattering / Extension Theory for Lattice Green's Functions / Part III: Many-Body Green's Functions - Field Operators and Three Pictures / Definition and Properties of Many-Body Green's Functions / The Diagram Technique for Zero-Temperature Green's Functions / Definition and Properties of Matsubara Green's Functions / Diagram Technique for the Matsubara Green's Functions / Three Approximation Schemes of the Diagram Technique / Linear Response Theory / The Equation of Motion Technique for the Green's Functions / Magnetic Systems Described by Heisenberg Model / The Green's Functions for Boson Systems with Condensation / Superconductors with Weak Interaction Between Electrons / Nonequilibrium Green's Functions / Electronic Transport through a Mesoscopic Structure / Appendixes / Index.

Chang Ho Choi, Joung Young Sug, Sang Don Choi +1 more

We prove that the relaxation functions in condensed matter physics can be easily calculated by the operator algebra technique in the continued fraction representation scheme. The Dyson equation for the single particle Green's function in the Hubbard model obtained in this way is identical with the one derived by Fedro and Willson in the lowest order approximation. And the cyclotron transition absorption formula obtained by this technique is identical with that of Argyres and Sigel.

John P. Killingbeck