Infrared behaviour of self-energy functions in the axial gauge

We discuss, in the axial gauge, the infrared singularities of the self-energy functions which determine the exponential of leading infrared divergencies in massles Yang-Mills theories.     

Cluster treatment of disordered systems

We formulate a cluster approximation to treat disordered systems following closely the well-known CPA. In contrast to other cluster theories a minimum of assumptions provides a selfconsistent theory which retains translational invariance and determines the structure of the self-energy uniquely.     

Scalar-tensor theories and the principle of equivalence

We investigate the restrictions on scalar-tensor theories of gravitation implied by the assumptions: (i) the field equations are derivable from an action principle, (ii) units of mass length and time are defined by atomic standards, and (iii) the principle of equivalence holds whenever gravitational self-energy can be neglected. We show that in all these theories the presence of gravitational energy in a system leads to violations of the principle of equivalence.     

Fermion masses and the extended technicolor scale

We show how the use of the so called irregular solution for the fermionic self-energy, enables to raise the extended technicolor mass scale, avoiding the problems of flavor changing neutral currents in dynamically broken gauge theories.     

On the exponentiation of leading infrared divergences in massless Yang-Mills theories

We derive, in the axial gauge, the effective U matrix which governs the behaviour of leading infrared singularities in the self-energy functions of Yang-Mills particles. We then show in a very simple manner, that these divergences, which determine the leading singularities in massless Yang-Mills theories, exponentiate.     

Properties of gluons in color superconductors

I give an introduction to color superconductivity in cold, dense quark matter. I focus in particular on how the solution to the gap equation is qualitatively different in ordinary BCS theory with local four-fermion interactions, in theories with non-local, but screened boson exchange, and in QCD, where magnetic gluon exchange is not screened at zero temperature. I argue that a reliable computation of the gap parameter requires knowledge of the gluon self-energy in a color superconductor. As a first step to determine the gluon self-energy, I report calculations of the Debye and Meissner masses in two- and three-flavor color superconductors.     

The singular seesaw mechanism with hierarchical Dirac neutrino mass

We evaluate the one-loop fermion self-energy for the gauged Thirring model in (2+1) dimensions, with one massive fermion flavor. We do this in the framework of the causal perturbation theory. In contrast to QED, the corresponding two-point function turns out to be infrared finite on the mass shell. Then, by means of a Ward identity, we derive the on-shell vertex correction and discuss the role played by causality for non-renormalizable theories. Received: 5 May 1999 / Published online: 27 January 2000     

Exponentiation of leading infrared divergences in massless Yang-Mills theories

In the Coulomb gauge, the leading infrared divergences of massless theories occur in external line self-energy parts only. This fact, together with the gauge invariance of S-matrix elements, leads to a simple proof of exponentiation.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Self-energy analysis of multiple-bosonic mode coupling in Sr2RuO4

We report angle-resolved photoemission spectroscopy studies on Sr₂RuO₄. We observe multiple-bosonic mode coupling in the α and β band dispersions. To extract the self-energy from the data for which the usual fitting methods do not work well, we propose a scheme that exploits the relation between the spectral intensity and self-energy, termed as relative self-energy. The relative self-energy obtained in that way contains important features of the self-energy. We observe not only the features that can be obtained from the band dispersions but also additional features that were not seen.     

Photon—Dyon Scattering in Non-Abelian Gauge Theory

We study the scattering of a non-Abelian dyon and photons. We demonstrate thattwo photons are necessary for Compton scattering of a non-Abelian dyon, throughS-matrix expansion. One of these two photons is associated with electric four-potentialand is ordinary, while the other is associated with magnetic four-potentialand is highly energetic and responsible for scattering of magnetic charge of thenon-Abelian dyon. We also study dyon—photon, dyon—dyon, and dyon—antidyonscattering and the self-energy of the dyon and both photons in non-Abeliangauge theories.     

Temperature dependence of the electron self-energy in a polar-crystal slab

In this paper we investigate temperature dependence of the electron self-energy in the polar-crystal slab using Green-function method. We introduce Q2D free Green's function for the first time. Numerical calculations of the electron self-energy using GaAs as an example are performed. The results show that the electron self-energy is a decreasing function of temperature. In calculation, we consider the effect of the excited states on the electron self-energy and find the ground-state energy be about 11% lower than that of bulk polaron. The results also imply that the high excited states pay a larger contribution to the electron self-energy with increasing temperature.     

Contributions to the self-energy of a wave propagating in a disordered array

We study the self-energy of a scalar wave propagating in a disordered static array of spherical scatterers. We employ the cluster expansion developed in a preceding article and provide detailed expressions for many contributions to the self-energy. The two-body term is covered completely. The three-body term is treated only in part, but we believe that those contributions which are important at not too high density are accounted for. Through resummation some of the contributions to the self-energy involve a large number of scatterers.     

THERMODYNAMICAL PROPERTIES OF GAUGE THEORIES AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

The plasma effects of gauge theories are investigated and the one-loop contributions to self-energy part of the photon at T≠0 and μ≠0 are calculated. It is shown that only electric fields give photon an effective mass, but magnetic fields don's contribute.     

Generalized Brückner-Hartree-Fock theory and self-consistent RPA

Self-consistent RPA (SCRPA) theory is developed in the particle-particle (pp) channel. It is pointed out that in this way vertex and self-energy corrections are taken into account on an equal footing whereas in Brückner-Hartree-Fock (BHF) this is not the case. We discuss in detail the interconnection between both theories and apply them to a model case. Excellent agreement with the exact solution is found for SCRPA where as BHF gives somewhat poorer results. In an appendix it is demonstrated how SCRPA connects to a variational principle and how, for the particle-hole case, sum rules and conservation laws are fulfilled.     

Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics

From the approximate chiral symmetry of QCD, it is known that the pion loops in chiral perturbation theory play a vital role in understanding the nucleon’s long-range structure. We demonstrate the equivalence of the light-front, equal-time and covariant formulations for the interactions of nucleons with pions in chiral perturbation theory. In particular, we discuss the self-energy Σ of a nucleon dressed by pion loops with the pseudovector πNN coupling. It is shown that the leading nonanalytic behavior of Σ is equivalent whichever formulations are used for the derivation. We also discuss the relation between the mass shift and the wavefunction renormalization as well as the difference between the pseudovector and pseudoscalar theories.     

The influence of many-body interactions on the de Haas-van Alphen effect

The de Haas-van Alphen (dHvA) effect, or Landau quantum oscillatory magnetization of metals, has been widely used to explore the single-particle aspects of electrons in metals with the aim of determining their Fermi surfaces. Its role in studying many-body effects in metals is less familiar, even though the influence of such interactions is well known. We present a general field-theoretic approach to this problem which shows that the paradigm for understanding the influence of many-body interactions in the dHvA effect should be shifted from the intuitively reasonable but potentially misleading arguments based on the electron self-energy on the real energy axis to an analysis of the self-energy along the imaginary energy axis. When viewed in this way, the dHvA effect assumes the role of a many-body self-energy filter in which the real part of the self-energy renormalizes the dHvA frequency while the imaginary part renormalizes independently the dHvA amplitude. We obtain a general theory for the dHvA effect in an interacting system which preserves the structure of the original non-interacting theory of Lifshitz and Kosevich. We then apply this extended Lifshitz-Kosevich theory to the analysis of several problems of interest, including electron-electron and electron-phonon interactions, heavy fermions and type II superconductors.     

Vacuum Polarization Tensor for QED in the Light Front Gauge

The use of light front coordinates in quantum field theories (QFT) always brought some problems and controversies. In this work we explore some aspects of its formalism with respect to the employment of dimensional regularization in the computation of the photon’s self-energy at the one-loop level and how the fermion propagator has an important role in the outcoming results.     

6s and 8d state self-energy for hydrogen-like ions and new results on the self-energy screening

We use a recently published method for the renormalization of the self-energy to calculate the self-energy of 6s and 8d levels to all orders in Zα. We demonstrate the accuracy of the method and its potential for high-n, low-Z applications. We also show that this method is perfectly suited for the evaluation of the two-electron self-energy (self-energy screening). For the first time, evaluation of the screening of the 1s electron by a second one in either the 1s,2s, 2p_1/2 or 2p_3/2 shells has been performed, for 30 ⩽ Z ⩽92. This revised version was published online in July 2006 with corrections to the Cover Date.