# nLab Walecka model

Contents

### Context

#### Fields and quanta

fields and particles in particle physics

and in the standard model of particle physics:

force field gauge bosons

scalar bosons

flavors of fundamental fermions in the
standard model of particle physics:
generation of fermions1st generation2nd generation3d generation
quarks ($q$)
up-typeup quark ($u$)charm quark ($c$)top quark ($t$)
down-typedown quark ($d$)strange quark ($s$)bottom quark ($b$)
leptons
chargedelectronmuontauon
neutralelectron neutrinomuon neutrinotau neutrino
bound states:
mesonslight mesons:
pion ($u d$)
ρ-meson ($u d$)
ω-meson ($u d$)
f1-meson
a1-meson
strange-mesons:
ϕ-meson ($s \bar s$),
kaon, K*-meson ($u s$, $d s$)
eta-meson ($u u + d d + s s$)

charmed heavy mesons:
D-meson ($u c$, $d c$, $s c$)
J/ψ-meson ($c \bar c$)
bottom heavy mesons:
B-meson ($q b$)
ϒ-meson ($b \bar b$)
baryonsnucleons:
proton $(u u d)$
neutron $(u d d)$

(also: antiparticles)

effective particles

hadrons (bound states of the above quarks)

solitons

in grand unified theory

minimally extended supersymmetric standard model

superpartners

bosinos:

dark matter candidates

Exotica

auxiliary fields

# Contents

## 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.

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

## 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:

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

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:

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)

### 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:

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)

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