Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part INormal Phase
- Part IIFermionic Superfluid Phase
- 21Time-Dependent BCS Hamiltonian and Gor’kov Equations
- 22The Hamiltonian in the Nambu Representation and the Role of the Hartree–Fock–BCS Self-Energy
- 23Contour-Ordered Green’s Functions in the Nambu Representation
- 24The T-matrix Approximation in the Superfluid Phase
- 25Derivation of the Time-Dependent Bogoliubov–deGennes Equations
- 26A Brief Excursus to the BCS–BEC Crossover
- 27Analytic Continuation from the Imaginary to the Real-Time Axis
- 28Derivation of the Time-Dependent Gross–Pitaevskii Equation for Composite Bosons in the BEC Limit of the BCS–BEC Crossover
- 29Derivation of the Time-Dependent Ginzburg–Landau Equation for Cooper Pairs in the BCS Limit of the BCS–BEC Crossover
- 30Real-Frequency Green’s Functions from the Kadanoff–Baym Equations in the Equilibrium Case
- 31Miscellany and Addenda to Part II
- Part IIIApplications
- Bibliography
- Index
27 - Analytic Continuation from the Imaginary to the Real-Time Axis
from Part II - Fermionic Superfluid Phase
Published online by Cambridge University Press: 06 February 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Author’s Note
- Part INormal Phase
- Part IIFermionic Superfluid Phase
- 21Time-Dependent BCS Hamiltonian and Gor’kov Equations
- 22The Hamiltonian in the Nambu Representation and the Role of the Hartree–Fock–BCS Self-Energy
- 23Contour-Ordered Green’s Functions in the Nambu Representation
- 24The T-matrix Approximation in the Superfluid Phase
- 25Derivation of the Time-Dependent Bogoliubov–deGennes Equations
- 26A Brief Excursus to the BCS–BEC Crossover
- 27Analytic Continuation from the Imaginary to the Real-Time Axis
- 28Derivation of the Time-Dependent Gross–Pitaevskii Equation for Composite Bosons in the BEC Limit of the BCS–BEC Crossover
- 29Derivation of the Time-Dependent Ginzburg–Landau Equation for Cooper Pairs in the BCS Limit of the BCS–BEC Crossover
- 30Real-Frequency Green’s Functions from the Kadanoff–Baym Equations in the Equilibrium Case
- 31Miscellany and Addenda to Part II
- Part IIIApplications
- Bibliography
- Index
Summary
This chapter reconsiders the original derivation of the Kadanoff and Baym equations, which relies on a procedure of analytic continuation from imaginary to real time in terms of an “extended” Matsubara approach. The procedure of analytic continuation proves useful for formal developments, like those to be considered in Chapters 28 and 29. The case when the system Hamiltonian does not depend on time is first treated, and the procedure is then extended under appropriate assumptions to the case when the Hamiltonian depends on time.
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- Many-Body Green's Functions for Time-Dependent Problems , pp. 225 - 234Publisher: Cambridge University PressPrint publication year: 2026
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