Symmetry energy in nuclear density functional theory

The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.Comment: 14 pages, 8 figures, submitted to the Special EPJA Issue on "Symmetry Energy

Analysis of Chiral Mean-Field Models for Nuclei

An analysis of nuclear properties based on a relativistic energy functional containing Dirac nucleons and classical scalar and vector meson fields is discussed. Density functional theory implies that this energy functional can include many-body effects that go beyond the simple Hartree approximation. Using basic ideas from effective field theory, a systematic truncation scheme is developed for the energy functional, which is based on an expansion in powers of the meson fields and their gradients. Chiral models are analyzed by considering specific lagrangians that realize the spontaneously broken chiral symmetry of QCD in different ways and by studying them at the Hartree level. Models that include a light scalar meson playing a dual role as the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon interaction, and which include a "Mexican-hat" potential, fail to reproduce basic ground-state properties of nuclei. In contrast, chiral models with a nonlinear realization of the symmetry are shown to contain the full flexibility inherent in the general energy functional and can therefore successfully describe nuclei.Comment: 47 pages, REVTeX 3.0 with epsf.sty, plus 12 figures in separate uuencoded compressed postscript fil

Symmetry transformations in Batalin-Vilkovisky formalism

This short note is closely related to Sen-Zwiebach paper on gauge transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate some conditions of physical equivalence of solutions to the quantum master equation and use these conditions to give a very transparent analysis of symmetry transformations in BV-approach. We prove that in some sense every quantum observable (i.e. every even function $H$ obeying $\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \endComment: 3 page

On the compatibility of causality and symmetry (Comments on "Analysis of causality in time-dependent density functional theory")

It is argued that there exists the only one inverse of the linear response function $\chi$, i.e. $\chi^{-1}$, which depends symmetrically of its spatial-times variables, see M.K. Harbola, and A. Banerjee, Phys. Rev. A {\bf 60}, 5101 (1999). Some brief comments on this consideration are presented. We show instead, that it is possible to construct the causal inverse also. At the same time we confirm the main statement of M.K. Harbola and A. Banerjee that in fact there is no contradiction between the symmetry and causality.Comment: 4 pages, LaTe

Geometric phases and hidden local gauge symmetry

The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases.Comment: 25 pages, 1 figure. Some typos have been corrected. To be published in Phys. Rev.

BRST Symmetric Formulation of a Theory with Gribov-type Copies

A path integral with BRST symmetry can be formulated by summing the Gribov-type copies in a very specific way if the functional correspondence between $\tau$ and the gauge parameter $\omega$ defined by $\tau (x) = f( A_{\mu}^{\omega})$ is ``globally single valued'', where $f( A_{\mu}^{\omega}) = 0$ specifies the gauge condition. A soluble gauge model with Gribov-type copies recently analyzed by Friedberg, Lee, Pang and Ren satisfies this criterion. A detailed BRST analysis of the soluble model proposed by the above authors is presented. The BRST symmetry, if it is consistently implemented, ensures the gauge independence of physical quantities. In particular, the vacuum (ground) state and the perturbative corrections to the ground state energy in the above model are analysed from a view point of BRST symmetry and $R_{\xi}$-gauge. Implications of the present analysis on some aspects of the Gribov problem in non-Abelian gauge theory, such as the $1/N$ expansion in QCD and also the dynamical instability of BRST symmetry, are briefly discussed.Comment: 30 pages plus 1 figur

Theoretical investigation of magnetoelectric effects in Ba2CoGe2O7

A joint theoretical approach, combining macroscopic symmetry analysis with microscopic methods (density functional theory and model cluster Hamiltonian), is employed to shed light on magnetoelectricity in Ba2CoGe2O7. We show that the recently reported experimental trend of polarization guided by magnetic field can be predicted on the basis of phenomenological Landau theory. From the microscopic side, Ba2CoGe2O7 emerges as a prototype of a class of magnetoelectrics, where the cross coupling between magnetic and dipolar degrees of freedom needs, as main ingredients, the on-site spin-orbit coupling and the spin-dependent O p - Co d hybridization, along with structural constraints related to the noncentrosymmetric structural symmetry and the peculiar configuration of CoO4 tetrahedrons.Comment: 5 pages, 4 figures, submitted for publicatio