R. J. Furnstahl, G. Rupak, T. Schaefer
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and then the varied frontiers of EFT for finite nuclei and nuclear matter are surveyed.
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The sigma meson mass and width are studied at finite baryonic density in the framework of a chiral unitary approach which successfully reproduces the meson meson phase shifts and generates the f0 and sigma resonances in vacuum.
We discuss the relation between the effective vector meson mass and equation of state (EOS) for nuclear matter. In the mean field approximation, the EOS becomes softer due to the reduction of the effective omega-meson mass, if we assume that the omega-meson mean field is proportional to the baryon density. We examine the assumption by using the auxiliary field method at finite temperature and /or density.
We derive practical three-body equations for the equal-time three-body Green function in matter. Our equations describe both bosons and fermions at finite density and temperature, and take into account all possible two-body sub-processes allowed by the underlying Hamiltonian.
In the article "On chiral symmetry restoration at finite density in large-$N_c$ QCD" by Adhikari, Cohen, Ayyagari and Strother [Phys. Rev. C 83, 065201 (2011)] the description of dense nuclear matter by means of Skyrmions in hyperspherical unit cells is severely criticized. We point out that this criticism is based on invalid assumptions and therefore unwarranted.
The spectral function for finite nuclei is computed within the framework of the Local Density Approximation, starting from nuclear matter spectral functions obtained with a realistic nucleon-nucleon interaction. The spectral function is decomposed into a single-particle part and a ''correlated'' part; the latter is treated in the local density approximation. As an application momentum distributions, quasi-particle strengths and overlap functions for valence hole states, and the light-cone momentum distribution in finite nuclei are computed.
We study the decay channels of the $Λ(1520)$ in a nuclear medium and find a sizable change - of the order of factor five - of the width of this hyperon at normal nuclear matter density. The mass shift of the $Λ(1520)$ is moderate.
The properties of $Σ$-hyperons in pure $Σ$ matter are studied with the finite-density quantum chromo-dynamics sum rule (QCDSR) approach. The $ΣΣ$ nuclear potential $U_Σ$ is most likely strongly attractive, it could be about -50 MeV or even more attractive at normal nuclear density. If this prediction is the case, the interactions between $Σ$-hyperons should play crucial roles in the strange nuclear matter, when there are multi-$Σ$ hyperons. The bound state of double-$Σ$ maybe exist.
In this work we calculate the equation of state of nuclear matter for different proton fractions at zero and finite temperature within the Thomas Fermi approach considering three different parameter sets: the well-known NL3 and TM1 and a density dependent parametrization proposed by Typel and Wolter. The main differences are outlined and the consequences of imposing beta-stability in these models are discussed.
This paper is devoted to the evaluation of the pionic scalar density at finite temperature and baryonic density. We express the latter effect in terms of the nuclear response evaluated in the random phase approxima- tion. We discuss the density and temperature evolution of the pionic density which governs the quark condensate evolution. Numerical evalua- tions are performed.
The spatial dependence of static meson correlation functions at finite baryon density is studied in the Nambu -- Jona - Lasinio model. In contrast to the finite temperature case, we find that the correlation functions at finite density are not screened but exhibit long-range oscillations. The observed phenomenon is analogous to the Friedel oscillations in a degenerate electron gas.
The speed of sound in QCD matter at finite temperature and density is investigated within the Polyakov loop improved Nambu--Jona-Lasinio (PNJL) model. The spinodal structure associated with the chiral first-order chiral phase transition is considered to describe the continuous variation of the speed of sound. The behaviors of the squared sound speed in different phases, including the stable, metastable and unstable phases, are derived. The relation between speed of sound and QCD phase transitions is systematically explored. In particular, the boundary of vanishing sound velocity is derived in …
Apparent inconsistencies between different formulations of nucleon sum rules at finite density are resolved through a proper accounting of asymmetries in the spectral functions between positive- and negative-energy states.
We show that at finite density pressure-pressure and current-current correlators exhibit divergences at $T_c$ owing to the fluctuations of the diquark field. Specifically, this leads to a significant excess of the soft photon production rate near $T_c$.
We study the baryon-quark phase transition in a molecular dynamics (MD) of quark degrees of freedom at finite temperature and density. The baryon state at low density and temperature, and the deconfined quark state at high density and temperature are reproduced. We investigate the equations of state of matters with different $u$-$d$-$s$ compositions. Then we draw phase diagrams in the temperature-density plane by this simulation. It is found that the baryon-quark transition is sensitive to the quark width.
We have studied the chiral soliton model in a thermal vacuum. The soliton equations are solved at finite temperature and density. The temperature or density dependent soliton solutions are presented. The physical properties of baryons are derived from the soliton solutions at finite temperature and density. The temperature or density dependent variation of the baryon properties are discussed.
We study the phase diagram of QCD at finite isospin density using two flavors of staggered quarks. We investigate the low temperature region of the phase diagram where we find a pion condensation phase at high chemical potential. We started a basic analysis of the spectrum at finite isospin density. In particular, we measured pion, rho and nucleon masses inside and outside of the pion condensation phase. In agreement with previous studies in two-color QCD at finite baryon density we find that the Polyakov loop does not depend on the density in the staggered formulation.
We note that the QCD phases at large finite density respect 't Hooft anomaly matching conditions. Specifically the spectrum of the light excitations possesses the correct quantum numbers required to obey global anomaly constraints. We argue that 't Hooft constraints can be used at finite density along with non perturbative methods to help selecting the correct phase.
For the linear sigma model with quarks we derive renormalization group flow equations for finite temperature and finite baryon density using the heat kernel cutoff. At zero temperature we evolve the effective potential to the Fermi momentum and compare the solutions of the full evolution equation with those in the mean field approximation. We find a first order phase transition either from a massive constituent quark phase to a mixed phase, where both massive and massless quarks are present, or from a metastable constituent quark phase at low density to a stable massless quark phase at high de…
We investigate the application of 't Hooft's anomaly matching conditions to gauge theories at finite matter density. We show that the matching conditions constrain the low-energy quasiparticle spectrum associated with possible realizations of global symmetries.
Effective field theory is applied to finite-density systems with an unnaturally large scattering length, such as neutron matter. A new organizational scheme is identified and connected with an expansion in inverse powers of the number of space-time dimensions. This power counting allows for analytic calculations in many-body systems and reproduces the hole-line expansion of traditional nuclear physics.
Reduction for one-loop tensor Feynman integrals in the relativistic quantum field theories at finite temperature and/or finite density
本文提出广义帕萨里诺-韦尔特曼约化方法，用于高效简化有限温度和/或有限密度下相对论量子场论中的单圈张量费曼积分，适用于夸克-胶子等离子体等系统。
Recent results of lattice QCD at finite temperature and density are reviewed. At vanishing density the transition temperature, the equation of state and hadron properties are discussed both for the pure gauge theory and for dynamical staggered, Wilson and overlap fermions. The second part deals with finite density. There are recent results for full QCD at finite temperature and moderate density, while at larger densities QCD-like models are studied.
I review the growing theoretical indications that at high densities color SU(3) gauge symmetry is spontaneously broken by the formation of a quark pair condensate. This leads to a rich phase structure for QCD as a function of temperature and chemical potential. I also discuss the prospects for lattice QCD calculations at finite density, including the Glasgow algorithm and imaginary chemical potential.
The Polyakov loop potential serves to distinguish between the confined hadronic and the deconfined quark-gluon plasma phases of QCD. For Nf=2+1 quark flavors with physical masses we determine the Polyakov loop potential at finite temperature and density and extract the location of the deconfinement transition. We find a cross-over at small values of the chemical potential running into a critical end-point at mu/T > 1.
This an English translation of a review of finite-density lattice QCD. The original version in Japanese appeared in Soryushiron Kenkyu Vol 31 (2020) No. 1.
Skyrmions at Finite Density
论文介绍通过推广球形刺猬拟设构建有限重子密度下非均匀强子凝聚体 Skyrme 模型精确解的新解析方法，并说明其可用于计算重要物理量。
QCD at finite temperature and density: Criticality
该研究概述有限温密下QCD临界点寻找的理论进展，涵盖格点QCD等方法，总结临界点位置的约束与预测，探讨未来挑战与机遇。
A path integration formulation for the finite density and temperature problems is shown to be consistent with the thermodynamics using an 8 component ``real'' representation for the fermion fields by applying it to a free fermion system. A relativistic quantum field theory is shown to be smoothly approached at zero temperature by a real-time thermal field theory so derived even at a finite density. The analysis leads to a new representation for the fermion fields which is shown to be inequivalent to the conventional 4 component theory at the quantum level by having a mirror universe with obser…
Quantum chromodynamics (QCD) at finite temperature (T), baryon chemical potential (\muB) and isospin chemical potential (\muI) is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, \muB and \muI. The phase structure in the space of T and \muB is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The e…
2-color QCD is the simplest QCD-like theory which is accessible to lattice simulations at finite density. It therefore plays an important role to test qualitative features and to provide benchmarks to other methods and models, which do not suffer from a sign problem. To this end, we determine the minimal-Landau-gauge propagators and 3-point vertices in this theory over a wide range of densities, the vacuum, and at both finite temperature and density. The results show that there is essentially no modification of the gauge sector in the low-temperature, low-density phase. Even outside this phase…
We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into SU(N). We used Euler angles decomposition for arbitrary N and the generalized hedgehog Ansatz at finite Baryon density. The Skyrmions of high topological charge that we find represent smooth Baryonic layers whose properties can be computed explicitly. In particular, we determine the energy to Baryon charge ratio for any N showing the smoothness of the large N limit. The closeness to the BPS bound of these configurations can also be analyzed. …
A relativistic quantum field theory is presented for finite density problems based on the principle of locality. It is found that, in addition to the conventional ones, a local approach to the relativistic quantum field theories at both zero and finite density consistent with the violation of Bell like inequalities should contain, and provide solutions to at least three additional problems, namely, 1) the statistical gauge invariance 2) the dark components of the local observables and 3) the fermion statistical blocking effects, base upon an asymptotic non-thermo ensemble. An application to mo…
We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian using Wilson fermions. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanical instability. This result is in qualitative agreement with continuum models and should be verifiable by future numerical simulations.
The equation of state of Hamiltonian lattice QCD at finite density is examined in the strong coupling limit by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the many body system. This solution exactly diagonalizes the Hamiltonian to second order in field operators for all densities and is used to evaluate the vacuum energy density from which we obtain the equation of state. We find that up to and beyond the chiral symmetry restoration density the pressure of the quark Fermi sea can be negative indicating its mechanica…
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