Correlations and the relativistic structure of the nucleon self-energy

A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the dependence of the single-particle energy on the small component in the Dirac spinors used to calculate the matrix elements of the underlying NN interaction. The resulting Dirac components of the self-energy depend on the momentum of the nucleons. At densities around and below the nuclear matter saturation density this momentum dependence is dominated by the non-locality of the Brueckner G matrix. At higher densities these correlation effects are suppressed and the momentum dependence due to the Fock exchange terms is getting more important. Differences between symmetric nuclear matter and neutron matter are discussed. Various versions of the Bonn potential are considered.Comment: 18 pages LaTeX, including 6 figure

Quasi-Spherical Light Cones of the Kerr Geometry

Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry that are asymptotic to Minkowski light cones at infinity. We develop the equations of these surfaces and examine their properties. In particular, we show that they are free of caustics for all positive values of the Kerr radial coordinate r. Useful applications include the propagation of high-frequency waves, the definition of Kruskal-like coordinates for a spinning black hole and the characteristic initial-value problem.Comment: LaTeX, 14 pages, 2 figure

Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei

The Dirac structure of the nucleon self-energy in asymmetric nuclear matter cannot reliably be deduced from the momentum dependence of the single-particle energies. It is demonstrated that such attempts yield an isospin dependence with even a wrong sign. Relativistic studies of finite nuclei have been based on such studies of asymmetric nuclear matter. The effects of these isospin components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include

Distributional Modes for Scalar Field Quantization

We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.Comment: 15 pages, RevTe

Scalar and vector decomposition of the nucleon self-energy in the relativistic Brueckner approach

We investigate the momentum dependence of the nucleon self-energy in nuclear matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the Bonn A potential. A strong momentum dependence of the scalar and vector self-energy components can be observed when a commonly used pseudo-vector choice for the covariant representation of the T-matrix is applied. This momentum dependence is dominated by the pion exchange. We discuss the problems of this choice and its relations to on-shell ambiguities of the T-matrix representation. Starting from a complete pseudo-vector representation of the T-matrix, which reproduces correctly the pseudo-vector pion-exchange contributions at the Hartree-Fock level, we observe a much weaker momentum dependence of the self-energy. This fixes the range of the inherent uncertainty in the determination of the scalar and vector self-energy components. Comparing to other work, we find that extracting the self-energy components by a fit to the single particle potential leads to even more ambiguous results.Comment: 35 pages RevTex, 7 PS figures, replaced by a revised and extended versio

The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.Comment: 16 pages, to appear in Phys. Rev.

Back Reaction Problem in the Inflationary Universe

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.Comment: 17 page

Renormalization Group Approach to Cosmological Back Reaction Problems

We investigated the back reaction of cosmological perturbations on the evolution of the universe using the second order perturbation of the Einstein's equation. To incorporate the back reaction effect due to the inhomogeneity into the framework of the cosmological perturbation, we used the renormalization group method. The second order zero mode solution which appears by the non-linearities of the Einstein's equation is regarded as a secular term of the perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant. For a dust dominated universe, using the second order gauge invariant quantity, we derived the renormalization group equation which determines the effective dynamics of the Friedman-Robertson-Walker universe with the back reaction effect in a gauge invariant manner. We obtained the solution of the renormalization group equation and found that perturbations of the scalar mode and the long wavelength tensor mode works as positive spatial curvature, and the short wavelength tensor mode as radiation fluid.Comment: 18 pages, revtex, to appear in Phys. Rev.

Affective iconic words benefit from additional sound–meaning integration in the left amygdala

Recent studies have shown that a similarity between sound and meaning of a word (i.e., iconicity) can help more readily access the meaning of that word, but the neural mechanisms underlying this beneficial role of iconicity in semantic processing remain largely unknown. In an fMRI study, we focused on the affective domain and examined whether affective iconic words (e.g., high arousal in both sound and meaning) activate additional brain regions that integrate emotional information from different domains (i.e., sound and meaning). In line with our hypothesis, affective iconic words, compared to their non‐iconic counterparts, elicited additional BOLD responses in the left amygdala known for its role in multimodal representation of emotions. Functional connectivity analyses revealed that the observed amygdalar activity was modulated by an interaction of iconic condition and activations in two hubs representative for processing sound (left superior temporal gyrus) and meaning (left inferior frontal gyrus) of words. These results provide a neural explanation for the facilitative role of iconicity in language processing and indicate that language users are sensitive to the interaction between sound and meaning aspect of words, suggesting the existence of iconicity as a general property of human language

Uniform approximation for diffractive contributions to the trace formula in billiard systems

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller's trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.Comment: LaTeX, 41 pages including 12 PostScript figures, submitted to Phys. Rev.