Self-consistent structure in a relativistic Dirac–Hartree–Fock approximation

Uechi, Hiroshi

doi:10.1016/s0375-9474(01)01139-3

Cited by 5 publications

(21 citation statements)

References 18 publications

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“…However, it is too complicated to extend beyond the mean-field (Hartree) approximation, because one has to deal complex mixings of nonlinear interactions. Therefore, it is appropriate to renormalize nonlinear self-interactions and introduce effective masses of mesons by employing the condition of conserving approximations [17,22], which will be discussed in the next section.…”

Section: The Nonlinear σ -ω With σ -ω Mixing Mean-field Approximationmentioning

confidence: 99%

“…The explicit relations between effective masses of mesons and nonlinear interactions are determined by the self-consistent condition of conserving approximations [17,22]. The functional derivative of energy density of the nonlinear mean-field approximation, E MFT , with respect to the particle distribution, n i , is given by…”

Section: The Effective Masses Of Mesons In the Nonlinear Mean-field Amentioning

confidence: 99%

“…It has been also applied to a variety of fields from semiconductors, plasmas and nuclear matter to high energy physics [18]. The theory has been applied to check self-consistency to approximations for nuclear matter, such as Hugenholtz-Van Hove theorem [19] (HV theorem), the virial theorem [20] and Gibbs relation in thermodynamics; the self-consistent conditions are denoted as thermodynamic consistency [21,22] to an approximation. Self-consistent, conserving and thermodynamically consistent approximations within the real-time formulation of nonequilibrium field theory are also discussed [23,24].…”

Section: Introductionmentioning

confidence: 99%

“…This is equivalent to the minimization of the ground state energy with respect to mean-fields of mesons at zero-temperature [7]. In this paper, the effective masses of mesons are naturally determined by the self-consistent condition of the theory of conserving approximations [17,18,22]. Effective masses of mesons are not merely definitions but essential physical quantities in order to maintain self-consistency to an approximation.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, at zero temperature, the functional derivative of energy density with respect to self-energy must vanish: δE/δΣ = 0 [17,22]. In articles, thermodynamic relations are ensured in terms of thermodynamic potential approach, however, the consistency of Green functions, self-energies and energy density is not often examined clearly, which is not complete as a thermodynamically consistent approximation.…”

Section: Introductionmentioning

confidence: 99%

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Properties of nuclear and neutron matter in a nonlinear σ–ω–ρ mean-field approximation with self- and mixed-interactions

Uechi

2006

Nuclear Physics A

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Properties of nuclear and neutron matter are discussed in a nonlinear σ -ω-ρ mean-field approximation with self-and mixed-interactions of mesons and baryons. The nonlinear interactions of mesons are naturally renormalized as effective masses of mesons by thermodynamic consistency required by the theory of conserving approximations. The nonlinear mean-field approximation results in a thermodynamically consistent approximation that maintains Hugenholtz-Van Hove theorem and Landau's requirement of quasiparticles, and it is generally proved that the nonlinear approximation is equivalent to the Hartree approximation with effective masses of baryons and mesons.The approximation is applied to nuclear and neutron matter, which suggests that the lower bound of nuclear compressibility, K ∼ 150 MeV, be required to be consistent with the binding energy (−15.75 MeV at k F = 1.30 fm −1 ) and the maximum mass of neutron stars (M max 2.00M ). Since the contributions of nonlinear interactions are strictly confined as the effective masses of mesons and baryons, properties of nuclear and neutron matter will enable us to study the validity of nonlinear interactions of mesons. The implication of thermodynamic consistency to the hypothesis of naturalness is discussed. The densitydependence of the compressibility, symmetry energy together with effective masses of hadrons will be important constraints for nonlinear mean-field approximations, and the accumulating data together with accurate measurements of observables in high density and energy region will supply significant information in order to testify theoretical consistency of nuclear models.

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Section: The Nonlinear σ -ω With σ -ω Mixing Mean-field Approximationmentioning

confidence: 99%

Section: The Effective Masses Of Mesons In the Nonlinear Mean-field Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Properties of nuclear and neutron matter in a nonlinear σ–ω–ρ mean-field approximation with self- and mixed-interactions

Uechi

2006

Nuclear Physics A

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Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy

Cai

Chen

2012

Physics Letters B

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Using the Hugenholtz-Van Hove theorem, we derive analytical expressions for the nuclear symmetry energy Esym(ρ) and its density slope L(ρ) in terms of the Lorentz covariant nucleon self-energies in isospin asymmetric nuclear matter. These general expressions are useful for determining the density dependence of the symmetry energy and understanding the Lorentz structure and the microscopic origin of the symmetry energy in relativistic covariant formulism. As an example, we analyze the Lorentz covariant nucleon self-energy decomposition of Esym(ρ) and L(ρ) and derive the corresponding analytical expressions within the nonlinear σ-ω-ρ-δ relativistic mean field model.

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Density-Dependent Properties of Hadronic Matter in an Extended Chiral (σ, π, ω) Mean-Field Model

Uechi¹,

Uechi²

2015

OALib

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Density-dependent relations among saturation properties of symmetric nuclear matter and hyperonic matter, the coupling ratios (strengths) of hyperon matter, and properties of hadronic stars are discussed by applying the conserving chiral nonlinear (σ, π, ω) hadronic mean-field theory. The chiral nonlinear (σ, π, ω) mean-field theory is an extension of the conserving nonlinear (nonchiral) σ-ω hadronic mean-field theory which is thermodynamically consistent, relativistic and is a Lorentz-covariant mean-field theory of hadrons. The extended chiral (σ, π, ω) mean-field model is one of effective models of Quantum Hadrodynamics (QHD). All the masses of hadrons are produced by the spontaneous chiral symmetry breaking, which is different from other conventional chiral partner models. By comparing both nonchiral and chiral mean-field approximations, the effects of the chiral symmetry breaking mechanism on the mass of σ-meson, coefficients of nonlinear interactions, coupling ratios of hyperons to nucleons and Fermi-liquid properties are investigated in nuclear matter, hyperonic matter, and neutron stars.

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Self-consistent structure in a relativistic Dirac–Hartree–Fock approximation

Cited by 5 publications

References 18 publications

Properties of nuclear and neutron matter in a nonlinear σ–ω–ρ mean-field approximation with self- and mixed-interactions

Properties of nuclear and neutron matter in a nonlinear σ–ω–ρ mean-field approximation with self- and mixed-interactions

Lorentz covariant nucleon self-energy decomposition of the nuclear symmetry energy

Density-Dependent Properties of Hadronic Matter in an Extended Chiral (σ, π, ω) Mean-Field Model

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