Order Self-energy Research Articles

Quasiparticle band structure of CdS.

Quasiparticle band structure calculations which include the most important cationic core states in the $\mathrm{GW}$ approximation of the self-energy operator are reported for a prototype II-VI semiconductor. The most salient feature of our results for cubic CdS is the finding that the complete cationic $N$ shell needs to be included in the pseudopotential and in the self-energy in order to obtain reasonable $\mathrm{GW}$ results in agreement with experiment.

Perturbation of tunneling processes by mechanical degrees of freedom in mesoscopic junctions.

We investigate the perturbation in the tunneling current caused by non-adiabatic mechanical motion in a mesoscopic tunnel junction. A theory introduced by Caroli et al. \cite{bi1,bi2,bi3} is used to evaluate second order self-energy corrections for this non-equilibrium situation lacking translational invariance. Inelastic signatures of the mechanical degrees of freedom are found in the current-voltage $I(V)$ characteristics. These give rise to sharp features in the derivative spectrum, $d^2I/dV^2$.

Second Order Selfenergy and Rate Equation in Time-Dependent Auger Processes

The Keldysh Green function formalism is employed to examine the validity of the rate equation description for time-dependent Auger type processes taking place in the ion- or metastable atom-surface collision such as Auger neutralization and metastable deexcitation. The second order selfenergy is considered in the Dyson equation, and the condition is expressed when the time-ordering operation is lifted

A comparison between the Mo/ller–Plesset and Green’s function perturbative approaches to the calculation of the correlation energy in the many-electron problem

The well-known expression for the total energy in terms of the single-particle many-body Green’s function is analyzed in detail. In particular the relation between the nth order Mo/ller–Plesset energy and the energy calculated from a Green’s function generated by the nth order self-energy is investigated. It is shown how the nth order Mo/ller–Plesset energy can be expressed in terms of the Green’s function. The H2 molecule is studied in a minimal basis to serve as a model in which exact results can be easily obtained. Numerical calculations are performed for H2, He, Be, LiH, Ne, HF, H2O, NH3, and CH4 and the results are analyzed in detail.

Nuclear response beyond mean field theory

An extension of the RPA equations is derived, with emphasis on the relation between the single-particle Green function and the polarization propagator. Including second order self-energy contributions the resulting particle-hole interaction includes the coupling to two-particle-two-hole (2p2h) states and the resulting response satisfies relevant conservation laws. This aspect of the theory is shown to be essential to obtain reliable and meaningful results for excitation strengths and to avoid ghost solutions. This method is applied to electromagnetic and charge exchange excitations in 48Ca up to 100 MeV. A G-matrix interaction based on meson exchange is used which takes care of short-range correlations. The results compare favourably with measured excitation strengths and electromagnetic form factors both at low energy as well as in the giant resonance region. Remaining discrepancies point in the direction of further strength reduction due to shortrange correlations as well as a possible stronger coupling to 2p2h states at low energy.

Second order U-perturbation approach to the Anderson lattice model in high dimensions

We study the periodic Anderson model (PAM), i.e. highly correlated, localized f-shells on a d-dimensional (simple-cubic) lattice hybridized with the states of a (tight-binding) conduction band. At least for the symmetric PAM (i.e. the unperturbed f-level energy E f and E f+U lie symmetric around the chemical potential, where U denotes the on-site Coulomb correlation between the f-electrons,) the second order (standard) U-perturbation treatment around the non-magnetic Hartree-Fock solution provides for a proper approximate treatment of the PAM even for relatively large values of U. In this communication we study this approach in the limit of high dimensions d of the underlying lattice. In this limit, which has recently been introduced by Metzner and Vollhardt for the Hubbard model, the selfenergy becomes site-diagonal, i.e. momentum independent, because of which the explicit calculation of the selfenergy in second order in U is much simpler than in lower dimensions. But one still obtains an f-electron spectral function, which shows all the properties, which are usually expected for heavy fermion systems, in particular single-particle peaks near to E f and E f+U, a strongly temperature dependent many-particle (Kondo) resonance peak near to the chemical potential, a hybridization (coherence) gap at the chemical potential, etc. Thus practical calculations may become much simpler for high d, but the essential physics remains the same as for realistic low d (=1,2,3).

Treatment of resonances with the dilated electron propagator: The 2P shape resonance in e-Mg scattering

The dilated electron propagator technique based on an underlying bivariational SCF and a second order self-energy is applied to study the 2P shape resonance in e-Mg scattering. Basis set effects are studied and comparisons with the results from an alternative construction of the second order dilated electron propagator are made.

Perturbation treatment of correlations in transition metals

Correlation effects in transition metals are treated within the Hubbard model by perturbation theory limited to second order in U/W (U : Coulomb integral; W : bandwidth). We have calculated the ground state total energy and the single particle self-energy in order to calculate the deformation of the one particle spectrum induced by these correlation effects. Finally some particular attention is paid to nickel.

Two-particle approximation for the quantum third virial coefficient: Comparison of two approaches

Two distinct approaches have been followed to produce an approximate expression for the third virial coefficient of a quantum system in terms of the pertinent two-particle quantities (standard T matrix elements and bound state eigenvalues and eigenstates): One approach is based on the T approximation for the self-energy in the theory of temperature Green functions, and the other uses the diagrams which represent the various terms in the multiple-scattering expansion of the three-particle T operator. It is shown that the result given by the former method is reproduced exactly by the contribution of a small number of selected diagrams. The Green function method requires the evaluation of the Kadanoff and Baym generalized T matrix to one order in the activity higher than its familiar low-density limit. The common result can be written entirely in terms of the lowest order self-energy and should give a reasonable approximation to the third virial coefficient for systems with short-range forces.

Influence of nonmagnetic impurities on the kondo effect

The influence of scattering by nonmagnetic impurities is studied in perturbation theory. While the finite lifetime of the electrons in intermediate states due to scattering by nonmagnetic impurities does not lead to a change in the logT-behaviour of the third-order self-energy, certain vertex-corrections give rise to an additional term which varies like 1/√T at low temperatures. Similar correction terms are found to occur in the higher order self-energy contributions. Although these terms diverge more strongly atT=0 than the logarithmic contributions they are quite small at finite temperatures since they depend on the lifetime τ of the electrons through a factor of (ɛ F τ)−5/2 (ɛ F Fermi energy). The possibility of observing these interference effects experimentally is discussed.

Die Propagatormethode in der Gitterraumtheorie

Keywords The Feynman diagrams and rules of a field theory with local four fermion coupling are transformed into a theory of interacting fermions in a finite dimensional Hilbert space constructed on Z3 points of a cubic lattice. The propagator is derived for the lattice space theory and the formal similarity and the qualitative differences are discussed and compared with conventional field theories. The mass produced by the interaction is calculated by compensation of the first order self-energy diagrams (Hartree-Fock-approximation). The solution for coupling constant W > 0 violates the chiral symmetry, the solution for W < 0 the cubic symmetry of the theory. The second order corrections to the mass operator are calculated. They diverge in the limit Z→∞ like if W is proportional to which is necessary for a finite mass in the HFapproximation. Under the same assumption the maximum divergence is like in any order of the perturbation theory. The mass operator is finite including second order contributions if W is proportional to . In this case the higher order contributions decrease like .

Exact First Order Self-Energy of a Lattice with Random Impurities

Exact First Order Self-Energy of a Lattice with Random Impurities

ON THE POSSIBLE EXISTENCE OF A DERIVATIVE COUPLING IN QUANTUM ELECTRODYNAMICS

Within the framework of quantum electrodynamics there exists the possibility of a derivative coupling between source and photon field, referred to as eΛ-charge, which has no classical analogue. For calculations the usual graph technique can be used, provided the factor eγμ contributed by each vertex in a conventional graph is replaced by ieΛkμ, where Λ is a length characteristic of the new interaction. Using as cutoff the nucleon mass M one finds for a bare source of electronic mass m the self-energy in second order to be Λm/m ≈ 200, if Λ−1 ≈ 60 M. It is argued that the large mass difference between muon and electron may be due to this effect, assuming muon and electron to differ only in that the muon has eΛ-charge whereas the electron has not. An estimate is made of the muon–muon scattering cross section caused by the presence of eΛ-charge on the muon, and it is found that the existence of this derivative coupling may have escaped observation.

Baryon Mass Spectrum

The possibility has been pointed out that if the relative parity between nucleons and particles is assumed to be odd, the lowest order self-energies of baryons coming from the charge-independent strong interaction give the observed baryon mass level ordering. Schwinger also suggested such a level splitting in a discussion of the isospace symmetry. It is shown that the numerical estimate of mass levels in the lowest order approximation is not inconsistent with the observation when reasonable magnitudes of the coupling constant g/sub k/ and of cut-off momentum are used. The baryon mass spectra obtained are graphically shown. (A.C.)

Note on Dieac's New Quantization Method in the Field Theory

universal validity for all kinds of wave fields accessible at present since, for example, the renormalization of an electric charge closely associated with the vacuum polarization has been shown to be entirely invalid in the vector meson theory4). Recently, Dirac's new methodS) of field quantization associated with the introduction of negative energy photon has been proposed with some success to remove the divergency of mass term in one electron theory. Although his theory has entirely failed to eliminate the mentioned divergency in the hole theory together with the . inclusion of another difficulty concerning the physical interpretation of negative probability, it seems to provide us a provisional but attractive footing for the future developnlent of the field theory since it is based on the quite natural generalization of the metric in Hilbert space upon which the mathematical scheme of the ordinary quantum mechanics has been formulated in a consistent way. In fact, if Pauli's qualitative consideration of Dirac's theory mentioned above were actually correct, the self-energy, to any degree of order, of an electron would be brought to vanish in one electron problem6), which fact seems to draw much attention in view of the present situation that the provi­ sional theories proposed so far are almost restricted merely to the second order self-energy. After all, since the merit or demerit of Dirac's new method of field quantization should be eventually criticized only through its application to the various kinds of physical phenomena in a close connection with the experimental results, we have here worked out the fourth order self-energy of a free electron and the Lamb-shift, i.e., the second order radiative reaction of a bound electron in hydrogen atom in order to provide a useful data for judging the physical

Notes on Dirac's New Quantization Method in the Field Theory

universal validity for all kinds of wave fields accessible at present since, for example, the renormalization of an electric charge closely associated with the vacuum polarization has been shown to be entirely invalid in the vector meson theory4). Recently, Dirac's new methodS) of field quantization associated with the introduction of negative energy photon has been proposed with some success to remove the divergency of mass term in one electron theory. Although his theory has entirely failed to eliminate the mentioned divergency in the hole theory together with the . inclusion of another difficulty concerning the physical interpretation of negative probability, it seems to provide us a provisional but attractive footing for the future developnlent of the field theory since it is based on the quite natural generalization of the metric in Hilbert space upon which the mathematical scheme of the ordinary quantum mechanics has been formulated in a consistent way. In fact, if Pauli's qualitative consideration of Dirac's theory mentioned above were actually correct, the self-energy, to any degree of order, of an electron would be brought to vanish in one electron problem6), which fact seems to draw much attention in view of the present situation that the provi­ sional theories proposed so far are almost restricted merely to the second order self-energy. After all, since the merit or demerit of Dirac's new method of field quantization should be eventually criticized only through its application to the various kinds of physical phenomena in a close connection with the experimental results, we have here worked out the fourth order self-energy of a free electron and the Lamb-shift, i.e., the second order radiative reaction of a bound electron in hydrogen atom in order to provide a useful data for judging the physical

On the self-energy of mesons

The self-energy of mesons is composed of contributions due to their interaction with the electromagnetic, the electron-neutrino and the nucleon field. Furthermore, if it is supposed that a particle creating an electromagnetic field also creates a short range neutral scalar field 1), the latter also contributes to the self-energy. The various first order self-energies are computed. For no kind of meson mutual compensations of the divergences by means of convergence relations is possible. § 1: Introduction. — § 2: Remarks on the electromagnetic self-energy. — § 3: The f-self-energy. — § 4: The electron-neutrinic and nucleic self-energy. — § 5: Discussion.