A self-consistent chiral Dirac-Hartree-Fock (CDHF) approximation generated by an effective model of the (σ, ω, π) quantum hadrodynamics (QHD) is extended to include Lorentz-scalar self-consistent vertex corrections. The scalar vertex corrections are constructed with self-consistency of QHD and Bethe-Salpeter equation, and the resulting vertex corrections are diagrammatically equivalent to self-consistent Hedin approximation, which is termed Hedin-Dirac-Hartree-Fock (HDHF) approximation. The effective model of the (σ, ω, π) quantum hadrodynamics maintains the requirement of thermodynamic consistency and density-functional theory (DFT) to a good approximation. The HDFT approximation is applied to properties of nuclear matter and neutron stars.
Cite this paper
Uechi, H. (2018). The Chiral Dirac-Hartree-Fock Approximation in QHD with Scalar Vertex Corrections. Open Access Library Journal, 5, e4739. doi: http://dx.doi.org/10.4236/oalib.1104739.
Serot, B.D. and Uechi, H. (1987) Neutron Stars in Relativistic Hadron-Quark Models. Annals of Physics, 179, 272. https://doi.org/10.1016/0003-4916(87)90137-0
Serot, B.D. and Walecka, J.D. (1992) Relativistic Nuclear Many-Body Theory. In: Ainsworth, T.L., Campbell, C.E., Clements, B.E. and Krotscheck, E., Eds., Recent Progress in Many-Body Theories, Vol. 3, Plenum, New York, p. 49. https://doi.org/10.1007/978-1-4615-3466-2_5
Serot, B.D. (2004) Covariant Effective Field Theory for Nuclear Structure and Nuclear Currents. Lecture Notes in Physics, 641, 31. https://doi.org/10.1007/978-3-540-39911-7_2
Uechi, H. (2006) Properties of Nuclear and Neutron Matter in a Nonlinear Mean-Field Approximation with Self- and Mixed-Interactions. Nuclear Physics A, 780, 247. https://doi.org/10.1016/j.nuclphysa.2006.10.015
Uechi, H. (2008) Density-Dependent Correlations between Properties of Nuclear Matter and Neutron Stars in a Nonlinear Mean-Field Approximation. Nuclear Physics A, 799, 181. https://doi.org/10.1016/j.nuclphysa.2007.11.003
Uechi, S.T. and Uechi, H. (2015) Hardon-Quark Hybrid Stars Constructed by the Nonlinear () Mean-Field Model and MIT-Bag Model. Open Access Library Journal, 2, e2012. https://doi.org/10.4236/oalib.1102012
Uechi, S.T. and Uechi, H. (2015) Density-Dependent Properties of Hadronic Matter in an Extended Chiral ( ) Mean-Field Model. Open Access Library Journal, 2, e2011. https://doi.org/10.4236/oalib.1102011
Uechi, S.T. and Uechi, H. (2016) Landau Theory of Fermi Liquid in a Relativistic Nonlinear (σ, ω) Model at Finite Temperature. Open Access Library Journal, 3, e2757. https://doi.org/10.4236/oalib.1102757
Müller, H. and Serot, B.D. (1996) Relativistic Mean-Field Theory and the High-Density Nuclear Equation of State. Nuclear Physics A, 606, 508-537. https://doi.org/10.1016/0375-9474(96)00187-X
Uechi, H., Uechi, S.T. and Serot, B.S. (2012) Neutron Stars: The Aspect of High Density Matter, Equations of State and Observables. Nova Science Publishers, New York.
Kohn, W. and Sham, L.J. (1965) Self-Consistent Equations Including Exchange and Correlation Effects. Physical Review, 140, A1133-A1138. https://doi.org/10.1103/PhysRev.140.A1133
Kohn, W. (1999) Nobel Lecture: Electronic Structure of Matter-Wave Functions and Density Functional. Reviews of Modern Physics, 71, 1253-1266. https://doi.org/10.1103/RevModPhys.71.1253
Takada, Y. (2001) Self-Energy Revision Operator Theory for the Many-Body Problem: Application to Dynamical Properties of the Elec-tron Gas. International Journal of Modern Physics B, 15, 2595. https://doi.org/10.1142/S0217979201006471
Uechi, H. (2004) The Theory of Conserving Approximations and the Density Functional Theory in Approximations for Nuclear Matter. Progress of Theoretical Physics, 111, 525. https://doi.org/10.1143/PTP.111.525
Uechi, S.T. and Uechi, H. (2017) Self-Consistent Many-Body Theory and Nuclear Matter in a Chiral Dirac-Hartree-Fock Approximation. Quarterly Physics Review, 3, 1-19.
Uechi, H. (1989) Fermi-Liquid Properties of Nuclear Matter in a Dirac-Hartree-Fock Approximation. Nuclear Physics A, 501, 813-834. https://doi.org/10.1016/0375-9474(89)90162-0
Uechi, H. (1992) Landau Fermi-Liquid Theory and Approximations in the Quantum Hadrodynamical Model. Nuclear Physics A, 541, 397-412. https://doi.org/10.1016/0375-9474(92)90183-K
Hugenholtz, N.M. and Van Hove, L. (1958) A Theorem on the Single Particle Energy in a Fermi Gas with Interaction. Physica, 24, 363-376. https://doi.org/10.1016/S0031-8914(58)95281-9
Takada, Y. (1995) Exact Self-Energy of the Many-Body Problem from Conserving Approximations. Physical Review B, 52, 12708-12719. https://doi.org/10.1103/PhysRevB.52.12708
Uechi, H. (1990) Constraints on the Self-Consistent Relativistic Fermi-Sea Particle Formalism in the Quantum Hadrodynamical Model. Physical Review C, 41, 744-752. https://doi.org/10.1103/PhysRevC.41.744
Uechi, H. (2001) Self-Consistent Structure in a Relativistic Dirac-Hartree-Fock Approximation. Nuclear Physics A, 696, 511-526. https://doi.org/10.1016/S0375-9474(01)01139-3
Takada, Y. (2001) Inclusion of Vertex Corrections in the Self-Consistent Calculation of Quasiparticles in Metals. Physical Review Letters, 87, Article ID: 226402. https://doi.org/10.1103/PhysRevLett.87.226402
Hedin, L. (1965) New Method for Calculating the One-Particle Green’s Function with Application to the Electron-Gas Problem. Physical Review, 139, A796-A823. https://doi.org/10.1103/PhysRev.139.A796
