nLab Walecka model

Idea

The Walecka model (also: QHD-I model) is an effective field theory related to chiral perturbation theory, that describes the residual strong nuclear force between baryons and specifically between nucleons, via exchange of sigma-mesons and omega-mesons, with the nucleons appearing as explicit effective fields (as opposed to emergent Skyrmion fields), as is more generally the case in baryon chiral perturbation theory. Some authors use the term quantum hadrodynamics specifically for the Walecka model of nuclear physics.

The inclusion also of pions and of rho-mesons into the Walecka model came to be known as quantum hadrodynamics, specifically QHD-II. See there for more.

Related concepts

effective field theories of nuclear physics, hence for confined-phase quantum chromodynamics:

• with effective ligh meson fields:

  • chiral perturbation theory

    • vector meson dominance

    • hidden local symmetry

  • with emergent (solitonic) baryon fields:

    • quark bag model

    • Skyrme model

    • Witten-Sakai-Sugimoto model

  • with explicit effective baryon fields:

    • baryon chiral perturbation theory

    • quantum hadrodynamics

      • Walecka model

  • with explicit quark fields:

    • quark-meson coupling model

References

Walecka hadrodynamics with nucleon fields

On quantum hadrodynamics (relativivist effective field theory of nuclear physics, coupling mesons and nucleons) in the sense of the Walecka model, hence with nucleons appearing as explicit fields (as opposed to being solitonic Skyrmions in the pion field as in chiral perturbation theory).

Precursor:

• Hans-Peter Duerr, Relativistic Effects in Nuclear Forces, Phys. Rev. 103, 469 (1956) (doi:10.1103/PhysRev.103.469)

The original Walecka model (QHD-I model), with nucleons coupled to sigma-mesons and omega-mesons:

• John Dirk Walecka, A Theory of highly condensed matter, Annals Phys. 83 (1974) 491 (spire:91609, dpi:10.1016/0003-4916(74)90208-5)

Inclusion into the Walecka model also of the pion and the rho-meson (the QHD-II model):

• Brian Serot, A relativistic nuclear field theory with $\pi$ and $\rho$ mesons, Physics Letters B Volume 86, Issue 2, 24 (1979), Pages 146-150 (doi:10.1016/0370-2693(79)90804-9)

• T Matsui, Brian Serot, The pion propagator in relativistic quantum field theories of the nuclear many-body problem, Annals of Physics Volume 144, Issue 1, November 1982, Pages 107-167 (doi:10.1016/0003-4916(82)90106-3)

Further discussion of these models:

• S. A. Chin, A relativistic many-body theory of high density matter, Annals of Physics Volume 108, Issue 2, October 1977, Pages 301-367 (doi:10.1016/0003-4916(77)90016-1)

• Brian Serot, John Dirk Walecka, The Relativistic Nuclear Many Body Problem, Adv. Nucl. Phys. 16 (1986) 1-327 (spire:207866)

• Brian Serot, Quantum hadrodynamics, Reports on Progress in Physics, Volume 55, Number 11 (1992) (doi:10.1088/0034-4885/55/11/001)

• Brian Serot, John Dirk Walecka, Chiral QHD with vector mesons, Acta Phys. Polon. B 23 (1992) 655-679 (spire:343513)

• Maciej Nowak, Mannque Rho, Ismail Zahed, Chiral Nuclear Dynamics, World Scientific 1996 (doi:10.1142/1681)

• Brian Serot, John Dirk Walecka, Recent Progress in Quantum Hadrodynamics, Int. J. Mod. Phys. E6:515-631, 1997 (arXiv:nucl-th/9701058)

• R. V. Poberezhnyuk, V. Vovchenko, D. V. Anchishkin, M. I. Gorenstein, Quantum van der Waals and Walecka models of nuclear matter (arXiv:1708.05605)

Further inclusion of electromagnetism (photon field):

• A. Yu. Korchin, D. Van Neck, M. Waroquier, Electromagnetic interaction in chiral quantum hadrodynamics and decay of vector and axial-vector mesons, Phys. Rev. C67 (2003) 015207 (arXiv:nucl-th/0302042)

Relation to quark-meson coupling model:

• Koichi Saito, Relationship between Quark-Meson Coupling Model and Quantum Hadrodynamics, Prog. Theor. Phys. 108 (2002) 609-614 (arXiv:nucl-th/0207053)

Hadrodynamics via Light-front QCD

On light-front QCD for quantum hadrodynamics:

• International Light Cone Advisory Committee, Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics, Nuclear Physics B - Proceedings Supplements Volumes 251–252, June–July 2014, Pages 165-174 (arXiv:1309.6333, doi:10.1016/j.nuclphysbps.2014.05.004)

• Edward Shuryak, Ismail Zahed, Hadronic structure on the light-front I: Instanton effects and quark-antiquark effective potentials (arXiv:2110.15927)

• Edward Shuryak, Ismail Zahed, Hadronic structure on the light-front II: QCD strings, Wilson lines and potentials (arXiv:2111.01775)

Baryon chiral perturbation theory

Discussion of baryon chiral perturbation theory, i.e of chiral perturbation theory with explicit effective (as opposed to or in addition to implicit skyrmionic) baryon fields included (see also Walecka model and quantum hadrodynamics):

Review:

• Ulf-G. Meissner, Chiral QCD: Baryon dynamics, in: At The Frontier of Particle Physics, pp. 417-505 (2001) (arxiv:hep-ph/0007092)

• Véronique Bernard, Chiral Perturbation Theory and Baryon Properties, Prog. Part. Nucl. Phys. 60:82-160, 2008 (arXiv:0706.0312)

• Stefan Scherer, Baryon chiral perturbation theory, PoS CD09:075, 2009 (arXiv:0910.0331)

Original articles:

• Elizabeth Jenkins, Aneesh V. Manohar, Baryon chiral perturbation theory using a heavy fermion lagrangian, Physics Letters B Volume 255, Issue 4, 21 February 1991, Pages 558-562 (doi:10.1016/0370-2693(91)90266-S)

• Robert Baur, Joachim Kambor, Generalized Heavy Baryon Chiral Perturbation Theory, Eur. Phys. J. C7:507-524, 1999 (arXiv:hep-ph/9803311)

Higher order terms:

• José Antonio Oller, Michela Verbeni, Joaquim Prades, Meson-baryon effective chiral Lagrangians to $\mathcal{O}(q^3)$, Journal of High Energy Physics, Volume 2006, JHEP09(2006) (arXiv:hep-ph/0608204, doi:10.1088/1126-6708/2006/09/079)

• Matthias Frink, Ulf-G. Meissner, On the chiral effective meson-baryon Lagrangian at third order, Eur. Phys. J. A29:255-260, 2006 (arXiv:hep-ph/0609256)

• Jose Antonio Oller, Joaquim Prades, Michela Verbeni, Meson-Baryon Effective Chiral Lagrangians at $\mathcal{O}(q^3)$ Revisited (arXiv:hep-ph/0701096, spire:742291)

See also:

• Lisheng Geng, Recent developments in $SU(3)$ covariant baryon chiral perturbation theory, Front. Phys., 2013, 8(3): 328-348 (arXiv:1301.6815)