Density Functional Aspects of Relativistic Field Theories

Engel, E.; Müller, Henrik Høeg; Speicher, Christoph; Dreizler, R. M.

doi:10.1007/978-1-4757-9975-0_5

Cited by 21 publications

(18 citation statements)

References 96 publications

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“…This is achieved by combining aspects of both density functional theory (DFT) [28][29][30][31] and effective field theory (EFT) [32][33][34]. In a DFT formulation of the relativistic nuclear many-body problem, the central object is an energy functional of scalar and vector densities (or more generally, vector four-currents).…”

Section: Typeset Using Revt E X I Introductionmentioning

confidence: 99%

Analysis of chiral mean-field models for nuclei

1996

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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. The utility of this approach relies on the observation that the large scalar and vector fields in nuclei are small enough compared to the nucleon mass to provide useful expansion parameters, yet large enough that exchange and correlation corrections to the fields can be treated as minor perturbations. Field equations for nuclei and nuclear matter are obtained by extremizing the energy functional with respect to the field variables, and inversion of these field equations allows one to express the unknown coefficients in the energy functional directly in terms of nuclear matter properties near equilibrium. This allows for a systematic * Present address: School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455.1 and complete study of the parameter space, so that parameter sets that accurately reproduce nuclear observables can be found, and models that fail to reproduce nuclear properties can be excluded. 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. The resulting energy functionals are special cases of the general functional considered earlier. 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 at the Hartree level. 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.

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Section: Typeset Using Revt E X I Introductionmentioning

confidence: 99%

Analysis of chiral mean-field models for nuclei

1996

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“…As for the HK theorem, however, the problem of radiative corrections has not been addressed until recently [9]. Thus, in the following, we briefly summarize the KS Although the functional dependence of T, on j p is not known explicitly, T , can be expressed exactly in terms of the single-particle four spinors p,,(x) resulting from a given local potential:…”

Section: Relativistic Density Functional Theorymentioning

confidence: 99%

“…On the other hand, UV divergencies that result from the perturbative treatment of the interaction between electrons and photons as well as the external potential show up in both the ground-state energy and the ground-state four current. These divergencies can be taken care of by the standard renormalization procedure of quantum field theory (applied to ground-state energies and four currents-see, e.g., [9]), the main point being that all counterterms required to keep the ground-state energy and four current finite are completely determined by specification of V p and do not explicitly depend on the ground state Iq) corresponding to V p . This then allows one to use the familiar nonrelativistic scheme [4] for the proof of the HK theorem also in the relativistic situation where any serious proof must be based on renormalized quantities (for details, see [ 9 ] ) .…”

Section: Field Theoretical Basismentioning

confidence: 99%

“…In particular, the existence of antiparticles (negative energy states) allowing for the creation of virtual electron-positron pairs and the intrinsically related question of renormalization have not been addressed. Recently, an attempt was made [9] to deal with these problems. The consequences, in particular for relativistic KS equations, will be briefly reviewed in this article.…”

Section: Introductionmentioning

confidence: 99%

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Density functional theory of field theoretical systems

Engel

1995

Int J of Quantum Chemistry

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“…This is achieved by combining aspects of both density functional theory [28][29][30][31] (DFT) and effective field theory [32][33][34] (EFT). In a DFT formulation of the relativistic nuclear many-body problem, the central object is an energy functional of scalar and vector densities (or more generally, vector four-currents).…”

Section: Energy Functional Analysis Of Mean-field Theories Of Nucleimentioning

confidence: 99%

Covariant Effective Field Theory for Bulk Properties of Nuclei

Serot

2003

Int. J. Mod. Phys. B

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Recent progress in Lorentz-covariant quantum field theories of the nuclear many-body problem (quantum hadrodynamics, or QHD) is discussed. The importance of modern perspectives in effective field theory and density functional theory for understanding the successes of QHD is emphasized. The inclusion of hadronic electromagnetic structure and of nonanalytic terms in the energy functional is also considered.

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Density Functional Aspects of Relativistic Field Theories

Cited by 21 publications

References 96 publications

Analysis of chiral mean-field models for nuclei

Analysis of chiral mean-field models for nuclei

Density functional theory of field theoretical systems

Covariant Effective Field Theory for Bulk Properties of Nuclei

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