Propagator, electron, renormalization

According to equation 15, eigenvalues of the superoperator Hamiltonian matrix, H, are poles (electron binding energies) of the electron propagator. Several renormalized methods can be defined in terms of approximate H matrices. The... 

Electron propagator theory generates a one-electron picture of electronic structure that includes electron correlation. One-electron energies may be obtained reliably for closed-shell molecules with the P3 method and more complex correlation effects can be treated with renormalized reference states and orbitals. To each electron binding energy, there corresponds a Dyson orbital that is a correlated generalization of a canonical molecular orbital. Electron propagator theory enables interpretation of precise ab initio calculations in terms of one-electron concepts. 

If there is no explicit external electromagnetic field, the covariant field equations determine a self-interaction energy that can be interpreted as a dynamical electron mass Sm. Since this turns out to be infinite, renormalization is necessary in order to have a viable physical theory. Field quantization is required for quantitative QED. The classical field equation for the electromagnetic field can be solved explicitly using the Green function or Feynman propagator GPV, whose Fourier transform is —gllv/K2, where k = kp — kq is the 4-momentum transfer. The product of y0 and the field-dependent term in the Dirac Hamiltonian, Eq. (10.3), is... 

The program has been tested on several QED and QCD motivated examples such as electron g — 2 in QED, gauge independence of the electron wave function renormalization in QED, a relation between the pole and the MS mass in QCD, exponentiation of the infra-red asymptotic of the heavy fermion propagator. Many details concerning these checks and other technical aspects of our calculations can be found in Ref. [11] which the interested reader should consult. 

Fig. 7. The graphical representation of the direct PWE renormalization approach. The double and ordinary solid lines with the cross denote the quadratic denominators in the bound and free electron propagators. The other notations axe the same as in Figure 5. The graphs a)-c) correspond to Eqs. (18)-(20) and the additional counterterm correspond to Eq. (21), respectively...

Keywords electron propagator quasiparticle approximations renormalized approximations quasiparticle virtual orbitals C60 fullerene ionization energies correlation states nucleotide electron detachment energies... 

Zakrzewski, V.G., Dolgounitcheva, O., Ortiz, J.V. Improved algorithms for renormalized electron propagator calculations. Int. J. Quantum Chem. 1999, 75, 607-14. 

Most of these diagrams contain two intermediate electron propagators and, therefore, double summations over the whole spectrum of the Dirac equation in the external nuclear field. This makes their computation numerically intensive. Both the selfenergy and vacuum-polarization screening corrections are ultraviolet divergent and require renormalization to yield a finite result. 

The T amplitudes contain infinite order contributions to each excitation level from the HF state. Thus, replacing the RSPT K amplitudes with the CC T amplitudes may be considered a renormalization procedure since certain classes of perturbation terms or diagrams are summed to infinite order. This idea was employed in work on both the electron propagator and the excitation propagator... 

It is seen how the interaction with the conduction electrons leads to a renormalization of the quadrupole susceptibility mq and hence of the phonon propagator. At this stage it is worth pointing out that there is a certain similarity between the effect of conduction electrons and of optical phonons. As will be shown later (see fig. 17.42) the diagrams for the renormalization of the acoustical phonons look the same except for the replacement of the electron-hole propagator x2iq, >) by the optical phonon propagator Do iq, to). 

Fig. 17.39. Renormalization of the phonon propagator due to the interaction Hac which leads to an indirect quadrupolar coupling of the RE-ions. Wavy lines are phonons, solid lines are conduction electrons and dashed lines denote the CEF-states.

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