Bethe-Salpeter equation function

On the other hand, functional derivatives of the Bethe-Salpeter equation allows to evaluate the nonlinear responses using the interaction kernels h only (which depend on the Hartree and exchange-correlation energies). The relations between the screened nonlinear responses and the bare ones are derived by using nonlinear PRF [32],... 

The account of two-particle correlations in nuclear matter can be performed considering the two-particle Green function in ladder approximation. The solution of the corresponding Bethe-Salpeter equation taking into account mean-field and Pauli blocking terms is equivalent to the solution of the wave equation... 

The most straightforward way refers to the Bethe-Salpeter equation, i.e. an equation for the two-body Green function. It may be solved for the Coulomb potential and a two-body perturbative theory can be developed starting from this solution. This method was rarely used in the bound state QED calculations, being very complicated. 

Gmn(r) is the one-exciton Green function. G(2) represents the time evolution of the two exciton states and satisfies the Bethe-Salpeter equation ... 

Fig. 10 Graphical representation of the inltomogenetnis Bethe-Salpeter equation (72). This is similar to Fig. 9 but operates now on the unperturbed wave function...

The first step toward a practical relativistic many-electron theory in the molecular sciences is the investigation of the two-electron problem in an external field which we meet, for instance, in the helium atom. Salpeter and Bethe derived a relativistic equation for the two-electron bound-state problem [135,170-173] rooted in quantum electrod)mamics, which features two separate times for the two particles. If we assume, however, that an absolute time is a good approximation, we arrive at an equation first considered by Breit [101,174,175]. The Bethe-Salpeter equation as well as the Breit equation hold for a 16-component wave function. From a formal point of view, these 16 components arise when the two four-dimensional one-electron Hilbert spaces are joined by direct multiplication to yield the two-electron Hilbert space. 

The chain is completed by relating the two-particle Green s function via the Bethe-Salpeter equation to the self-energy... 

Note that G/ r refers to the full one-particle Green s function. Eq. (2.10) is an integral equation, but if the kernel K(iA> iAL-Uk) depends only on CJ> the Bethe-Salpeter equation would reduce to a Dyson s equation ... 

Quantum field theory provides an unambiguous way to find energy levels of any composite system. They are determined by the positions of the poles of the respective Green functions. This idea was first realized in the form of the Bethe-Salpeter (BS) equation for the two-particle Green function (see Fig. 1.2)... 

Bethe and Salpeter [24] as well as Gell-Mann and Low [21] argue that a similar equation can be set up for a two-particle wave function. We assume we have a singlereference situation and let the Dyson equation act on the unperturbed wave function of model function (xo, Xq) (with to = t o = -oo). With... 

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