Book contents
- Frontmatter
- Contents
- Preface
- List of abbreviations and acronyms
- Fundamental constants and basic relations
- 1 Second quantization
- 2 Getting familiar with second quantization: model Hamiltonians
- 3 Time-dependent problems and equations of motion
- 4 The contour idea
- 5 Many-particle Green's functions
- 6 One-particle Green's function
- 7 Mean field approximations
- 8 Conserving approximations: two-particle Green's function
- 9 Conserving approximations: self-energy
- 10 MBPT for the Green's function
- 11 MBPT and variational principles for the grand potential
- 12 MBPT for the two-particle Green's function
- 13 Applications of MBPT to equilibrium problems
- 14 Linear response theory: preliminaries
- 15 Linear response theory: many-body formulation
- 16 Applications of MBPT to nonequilibrium problems
- Appendices
- References
- Index
6 - One-particle Green's function
Published online by Cambridge University Press: 05 March 2013
- Frontmatter
- Contents
- Preface
- List of abbreviations and acronyms
- Fundamental constants and basic relations
- 1 Second quantization
- 2 Getting familiar with second quantization: model Hamiltonians
- 3 Time-dependent problems and equations of motion
- 4 The contour idea
- 5 Many-particle Green's functions
- 6 One-particle Green's function
- 7 Mean field approximations
- 8 Conserving approximations: two-particle Green's function
- 9 Conserving approximations: self-energy
- 10 MBPT for the Green's function
- 11 MBPT and variational principles for the grand potential
- 12 MBPT for the two-particle Green's function
- 13 Applications of MBPT to equilibrium problems
- 14 Linear response theory: preliminaries
- 15 Linear response theory: many-body formulation
- 16 Applications of MBPT to nonequilibrium problems
- Appendices
- References
- Index
Summary
In this chapter we get acquainted with the one-particle Green's function G, or simply the Green's function. The chapter is divided in three parts. In the first part (Section 6.1) we illustrate what kind of physical information can be extracted from the different Keldysh components of G. The aim of this first part is to introduce some general concepts without being too formal. In the second part (Section 6.2) we calculate the noninteracting Green's function. Finally in the third part (Sections 6.3 and 6.4) we consider the interacting Green's function and derive several exact properties. We also discuss other physical (and measurable) quantities that can be calculated from G and that are relevant to the analysis of the following chapters.
What can we learn fromG?
We start our overview with a preliminary discussion on the different character of the space– spin and time dependence in G(1; 2). In the Dirac formalism the time-dependent wavefunction Ψ(x, t) of a single particle is the inner product between the position–spin ket |x〉 and the time evolved ket |Ψ(t)〉. In other words, the wavefunction Ψ(x, t) is the representation of the ket |Ψ(t)〉 in the position–spin basis.
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- Nonequilibrium Many-Body Theory of Quantum SystemsA Modern Introduction, pp. 153 - 204Publisher: Cambridge University PressPrint publication year: 2013