Effective field theory for dilute Fermi systems

Hammer, H. W.; Furnstahl, R. J.

doi:10.1016/s0375-9474(00)00325-0

Cited by 125 publications

(279 citation statements)

References 28 publications

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“…Since only doubleintegrals are involved the other numerical coefficients can be obtained with high precision. One finds again good agreement with existing calculations [4,7,9]. The third order coefficient is: 0.0861836 − 0.0106103 = 0.0640627 + 0.0115106, where the numbers on the left hand side correspond to our separation R 2 − π 2 I 2 /3 and those on the right side refer to the sum of two-fold particle-particle and two-fold hole-hole rescatterings.…”

Section: Expansion In Powers Of Ak Fsupporting

confidence: 88%

Resummation of fermionic in-medium ladder diagrams to all orders

Kaiser

2011

Nuclear Physics A

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A system of fermions with a short-range interaction proportional to the scattering length a is studied at finite density. At any order a n , we evaluate the complete contributions to the energy per particleĒ(k f ) arising from combined (multiple) particle-particle and hole-hole rescatterings in the medium. This novel result is achieved by simply decomposing the particle-hole propagator into the vacuum propagator plus a mediuminsertion and correcting for certain symmetry factors in the (n − 1)-th power of the in-medium loop. Known results for the low-density expansion up to and including order a 4 are accurately reproduced. The emerging series in ak f can be summed to all orders in the form of a double-integral over an arctangent function. In that representation the unitary limit a → ∞ can be taken and one obtains the value ξ = 0.5067 for the universal Bertsch parameter. We discuss also applications to the equation of state of neutron matter at low densities and mention further extensions of the resummation method.

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Section: Expansion In Powers Of Ak Fsupporting

confidence: 88%

Resummation of fermionic in-medium ladder diagrams to all orders

Kaiser

2011

Nuclear Physics A

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“…We proceed now with a central theme of our work: establishing connections between the density-dependent point couplings in (10)(11)(12)(13)(14)(15) and constraints from QCD. Two key features of low-energy, non perturbative QCD are at the origin of this discussion: the presence of a non-trivial vacuum characterized by strong condensates and the important role of pionic fluctuations governing the low-energy, long wavelength dynamics according to the rules imposed by spontaneously broken chiral symmetry.…”

Section: Qcd Constraintsmentioning

confidence: 99%

“…We therefore include pions as explicit degrees of freedom in the description of nuclear many-body dynamics. Hammer and Furnsthal [14] pointed out earlier that an effective field theory of dilute Fermi systems must include pions for a proper description of the long-range physics. We support this statement by explicit calculations.…”

Section: Introductionmentioning

confidence: 99%

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

et al. 2004

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We derive a microscopic relativistic point-coupling model of nuclear many-body dynamics constrained by in-medium QCD sum rules and chiral symmetry. The effective Lagrangian is characterized by density dependent coupling strengths, determined by chiral one-and two-pion exchange and by QCD sum rule constraints for the large isoscalar nucleon self-energies that arise through changes of the quark condensate and the quark density at finite baryon density. This approach is tested in the analysis of the equations of state for symmetric and asymmetric nuclear matter, and of bulk and single-nucleon properties of finite nuclei. In comparison with purely phenomenological mean-field approaches, the built-in QCD constraints and the explicit treatment of pion exchange restrict the freedom in adjusting parameters and functional forms of density dependent couplings. It is shown that chiral (two-pion exchange) fluctuations play a prominent role for nuclear binding and saturation, whereas strong scalar and vector fields of about equal magnitude and opposite sign, induced by changes of the QCD vacuum in the presence of baryonic matter, generate the large effective spin-orbit potential in finite nuclei.

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“…This is the standard low density expansion for a hard sphere Fermi gas which was studied by Huang, Lee and Yang in the 1950's and rederived in the EFT context by Hammer and Furnstahl [6,13,14]. In real nuclear matter, however, |k F a| ≫ 1 and the perturbative low density expansion is not useful.…”

Section: Introductionmentioning

confidence: 99%

“…In this work we wish to study the EFT approach to the nuclear many body problem [6,7,8,9,10,11,12]. We will focus on the equation of state of pure neutron matter at low to moderate density, a problem that is of relevance to the structure of neutron stars.…”

Section: Introductionmentioning

confidence: 99%

Many body methods and effective field theory

2005

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In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and particle-hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (k F a) → ∞ and (k F r) → 0, where k F is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space-time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.

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Effective field theory for dilute Fermi systems

Cited by 125 publications

References 28 publications

Resummation of fermionic in-medium ladder diagrams to all orders

Resummation of fermionic in-medium ladder diagrams to all orders

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

Many body methods and effective field theory

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