Self-Consistent Approximations in Many-Body Systems

Baym, Gordon

doi:10.1103/physrev.127.1391

Cited by 1,374 publications

(1,529 citation statements)

References 12 publications

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“…Baym and Kadanoff have shown that an approximation chosen for Γ 4−pt should be such that parts a) and b) in Fig. 4 generate the same self-energy [28] - [30]. With this symmetry requirement it is assured that the solution of the Dyson equation g(ω) satifies basic conservation laws, such as particle number, total energy, total momentum, and total angular momentum.…”

Section: Equation Of Motion Methods and Dyson Equationmentioning

confidence: 99%

Self-consistent Green's function method for nuclei and nuclear matter

Dickhoff

Barbieri

2004

Progress in Particle and Nuclear Physics

494

599

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Recent results obtained by applying the method of self-consistent Green's functions to nuclei and nuclear matter are reviewed. Particular attention is given to the description of experimental data obtained from the (e,e ′ p) and (e,e ′ 2N) reactions that determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single-particle and two-particle propagators. For this reason and the fact that these amplitudes can now be calculated with the inclusion of all the relevant physical processes, it is useful to explore the efficacy of the method of self-consistent Green's functions in describing these experimental data. Results for both finite nuclei and nuclear matter are discussed with particular emphasis on clarifying the role of short-range correlations in determining various experimental quantities. The important role of long-range correlations in determining the structure of lowenergy correlations is also documented. For a complete understanding of nuclear phenomena it is therefore essential to include both types of physical correlations. We demonstrate that recent experimental results for these reactions combined with the reported theoretical calculations yield a very clear understanding of the properties of all protons in the nucleus. We propose that this knowledge of the properties of constituent fermions in a correlated many-body system is a unique feature of nuclear physics.

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Section: Equation Of Motion Methods and Dyson Equationmentioning

confidence: 99%

Self-consistent Green's function method for nuclei and nuclear matter

Dickhoff

Barbieri

2004

Progress in Particle and Nuclear Physics

494

599

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“…Within the validity of the non-relativistic approximation for fermions, one has 2 √ J s ≪ m f . Then from (15) and (72) we find…”

Section: Boson Spectrum In the Regime Of Non-relativistic Fermions Pmentioning

confidence: 99%

“…In sect. 2 we introduce a Φ approach of Baym [15] and its application to the description of the system of coupled fermions and bosons. Technical details of the formalism: relations between Green functions and self-energies and the scheme of the particle-antiparticle separation are deferred to the Appendix A. Sects 3 and 4 are key sections of our study.…”

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confidence: 99%

Hadron liquid with a small baryon chemical potential at finite temperature

Voskresensky¹

2004

Nuclear Physics A

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We discuss general properties of a system of heavy fermions (including antiparticles) interacting with rather light bosons. First, we consider one diagram of Φ. The fermion chemical potential is assumed to be small, µ f < ∼ T . Already for the low temperature, T ≪ min(T bl.f , m b ), the fermion mass shell proves to be partially blurred due to multiple fermion rescatterings on virtual bosons, m b is the boson mass, T bl.f (≪ m f ) is the typical temperature corresponding to a complete blurring of the gap between fermion-antifermion continua, m f is the fermion mass. As the result, the ratio of the number of fermion-antifermion pairs to the number provided by the ordinary Boltzmann distribution becomes larger than unity (is the effective boson mass, the abundance of all particles dramatically increases. Bosons behave as quasi-static impurities, on which heavy fermions undergo multiple rescatterings. The soft thermal loop approximation solves the problem. The effective fermion mass m * f (T ) decreases with the temperature increase. For T > ∼ T bl.f fermions are essentially relativistic particles. Due to the interaction of the boson with fermion-antifermion pairs, m * b (T ) decreases leading to the possibility of the "hot Bose condensation" for T > T cb . The phase transition might be of the second order or of the first order depending on the species under consideration. We study in detail properties of the system of spin 1/2 heavy fermions interacting with substantially lighter scalar neutral bosons (e.g., N σ system). Correlation effects of higher order diagrams of Φ are evaluated resulting in a suppression of vertices for T > ∼ m * b (T ). The abundance of high-lying baryon resonances proves to be of the same order, as the nucleon-antinucleon abundance, or might be even higher for some species. Further we discuss the system of heavy fermions interacting with more light vector bosons (e.g., N ω and N ρ) and then, with pseudo-scalar bosons (e.g., N π). For the fermion -vector boson system correlation effects are incorporated by keeping the Ward identity. In case of the fermion -pseudo-scalar boson system correlation effects are rather small. Finally, we allow for all interactions. We estimate R N ∼ 1.5 for T ∼ m π /2; T bl.f proves to be near T cb ; both values are in the vicinity of the pion mass m π .

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“…We may determine the additive constant V eff (φ = 0) in (6.2), by choosing the boundary condition of the differential equation (6.1) at φ = 0, such that the thermodynamic consistency of our formalism remains valid in the sense discussed first by Baym in [40]. Specifically, we require that the grand-canonical potential Ω(V, T, µ) calculated from the symmetry-improved effective action Γ[φ, ∆] as 6) where V ≡ x is the volume of the system, coincides with the one obtained by…”

Section: Minimally Symmetry-improved Cjt Effective Potentialmentioning

confidence: 99%

Symmetry-improved CJT effective action

2013

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The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O (2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetryimproved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.

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Self-Consistent Approximations in Many-Body Systems

Cited by 1,374 publications

References 12 publications

Self-consistent Green's function method for nuclei and nuclear matter

Self-consistent Green's function method for nuclei and nuclear matter

Hadron liquid with a small baryon chemical potential at finite temperature

Symmetry-improved CJT effective action

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