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RESEARCH PRODUCT

One-particle Green's function

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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 from G ? 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.