Based on the Dyson-Schwinger equations of quark propagator in rainbow truncation with an effective gluonpropagator,the ten unknown Gasser-Leutwyler coefficients of the chiral Lagrangian for pseudoscalar Goldstone boso...Based on the Dyson-Schwinger equations of quark propagator in rainbow truncation with an effective gluonpropagator,the ten unknown Gasser-Leutwyler coefficients of the chiral Lagrangian for pseudoscalar Goldstone bosonsare predicted.The predicted values of L_i with i=1,2,...,10 are in a reasonable agreement with empirical values usedwidely in literature,and the values predicted by many other theoretical models with QCD characteristics.展开更多
We use the Schwinger-boson approach to study the anisotropy ferrimagnetic spin-（1/2,1） chain with bond alternation.Based on the effect of bond alternation δ,we obtain energy gap,free energy,and specific heat,respec...We use the Schwinger-boson approach to study the anisotropy ferrimagnetic spin-（1/2,1） chain with bond alternation.Based on the effect of bond alternation δ,we obtain energy gap,free energy,and specific heat,respectively.The specific heat with larger bond alternation（δ 〉 0.7） displays a peak at low temperature.Based on the effect of XXZ anisotropy parameter Δ,we present excited spectrums,free energy,and specific heat,respectively.展开更多
Based on the Dyson–Schwinger equations of QCD in the 'rainbow' approximation, the fully dressed quark propagator is investigated, and then an algebraic parametrization form of the propagator is obtained as a...Based on the Dyson–Schwinger equations of QCD in the 'rainbow' approximation, the fully dressed quark propagator is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes and built up the fully dressed quark propagator and the dynamical running masses defined by and for light quarks u, d and s are calculated, respectively. Using the predicted running masses , quark condensates for u, d quarks, and for s quark, and experimental pion decay constant , the masses of Goldstone bosons K, π, and η are also evaluated. The numerical results show that the masses of quarks are dependent on their momentum . The fully dressed quark amplitudes and have correct behaviors which can be used for many purposes in our future researches on nonperturbative QCD.展开更多
In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., t...In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.展开更多
By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equati...By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.展开更多
The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark...The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark energy via a golden mean scaling-super quantization of the electromagnetic field.展开更多
The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.
As a topic of “quantum color dynamics”, we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First...As a topic of “quantum color dynamics”, we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size R is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size R is taken to be smaller than a hadron, R ~ 1 fm, and larger than a constituent quark, R ~ 0.3 fm. We find that the compact diquark with R ~ 0.3 fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect.展开更多
In view of the properties of mesons in hot strongly interacting matter, the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladd...In view of the properties of mesons in hot strongly interacting matter, the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladder approximation are analysed in some detail. In Euclidean space within the Matsubara imaginary time formalism, the quark propagator is not longer a O(4) symmetric function and possesses a discrete spectrum of the fourth component of the momentum. This makes the treatment of the Dyson-Schwinger and Bethe-Salpeter equations conceptually different from the vacuum and technically much more involved. The question whether the interaction kernel known from vacuum calculations can be applied at finite temperatures remains still open. We find that, at low temperatures, the model interaction with vacuum parameters provides a reasonable description of the quark propagator, while at temperatures higher than a certain critical value T<sub>c </sub>the interaction requires stringent modifications. The general properties of the quark propagator at finite temperatures can be inferred from lattice QCD (LQCD) calculations. We argue that, to achieve a reasonable agreement of the model calculations with that from LQCD, the kernel is to be modified in such a way as to screen the infra-red part of the interaction at temperatures larger than T<sub>c </sub>. For this, we analyse the solutions of the truncated Dyson-Schwinger equation with existing interaction kernels in a large temperature range with particular attention on high temperatures in order to find hints to an adequate temperature dependence of the interaction kernel to be further implemented in the Bethe-Salpeter equation for mesons. This will allow investigating the possible in medium modifications of the meson properties as well as the conditions of quark deconfinement in hot matter.展开更多
We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the struct...We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.展开更多
We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes.We compute the potential between the produced pair by evaluating the classical action of a string attached on a ...We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes.We compute the potential between the produced pair by evaluating the classical action of a string attached on a probe D3-brane at an intermediate position in the AdS bulk.We find that increasing the angular momentum reduces the potential barrier,thus enhancing the Schwinger effect,consistent with previous findings obtained via the local Lorentz transformation.In particular,these effects are more visible for the particle pair lying in the transversal plane compared with that along the longitudinal orientation.In addition,we discuss how the Schwinger effect changes with the shear viscosity to entropy density ratio at strong coupling under the influence of angular momentum.展开更多
基金supported in part by National Natural Science Foundation of China under Grant Nos.10647002 and 10565001the Natural Science Foundation of Guangxi under Grant Nos.0542042,0481030,and 0575020
文摘Based on the Dyson-Schwinger equations of quark propagator in rainbow truncation with an effective gluonpropagator,the ten unknown Gasser-Leutwyler coefficients of the chiral Lagrangian for pseudoscalar Goldstone bosonsare predicted.The predicted values of L_i with i=1,2,...,10 are in a reasonable agreement with empirical values usedwidely in literature,and the values predicted by many other theoretical models with QCD characteristics.
基金supported by the National Natural Science Foundation of China(Grant No.10774035)the Qianjiang RenCai Program of Zhejiang Province,China(Grant No.2007R0010)
文摘We use the Schwinger-boson approach to study the anisotropy ferrimagnetic spin-（1/2,1） chain with bond alternation.Based on the effect of bond alternation δ,we obtain energy gap,free energy,and specific heat,respectively.The specific heat with larger bond alternation（δ 〉 0.7） displays a peak at low temperature.Based on the effect of XXZ anisotropy parameter Δ,we present excited spectrums,free energy,and specific heat,respectively.
文摘Based on the Dyson–Schwinger equations of QCD in the 'rainbow' approximation, the fully dressed quark propagator is investigated, and then an algebraic parametrization form of the propagator is obtained as a solution of the equations. The dressed quark amplitudes and built up the fully dressed quark propagator and the dynamical running masses defined by and for light quarks u, d and s are calculated, respectively. Using the predicted running masses , quark condensates for u, d quarks, and for s quark, and experimental pion decay constant , the masses of Goldstone bosons K, π, and η are also evaluated. The numerical results show that the masses of quarks are dependent on their momentum . The fully dressed quark amplitudes and have correct behaviors which can be used for many purposes in our future researches on nonperturbative QCD.
基金The project supported in part by National Natural Science Foundation of China under Grant No.10575050the Research Fund for the Doctoral Program of Higher Education under Grant No.20060284020
文摘In quantum chromodynamics （QCD）, the scalar susceptibility represents the modification of the quark condensate, to a small perturbation of the parameter responsible for the explicit breaking of the symmetry, i.e., the current quark mass. By studying the linear response of the dressed quark propagator to the presence of a nonzero quark mass, we derive a model-independent formula for the scalar susceptibility, which contains the dressed quark propagator G（p） and the dressed scalar vertex F（p, 0）. The numerical values of the scalar susceptibility Xs are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach by employing two typical forms of model gluon propagator.
文摘By means of a formal expression of Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperatures and finite quark chemical potentials, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by A（p^2）ψ - B（p^2）, we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A（p^2） = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.
文摘The present paper utilizes the similarity between the non-perturbative Julian Schwinger-Efimov-Fredkin approach and that of E-infinity Cantorian spacetime theory to give an exact solution to the problem of cosmic dark energy via a golden mean scaling-super quantization of the electromagnetic field.
文摘The pion and tensor vacuum susceptibilities are calculated in the framework of the renormalizable DysonSchwinger equations. A comparison with the results of other nonperturbative QCD approaches is given.
文摘As a topic of “quantum color dynamics”, we study various mass generation of colored particles and gluonic dressing effect in a non-perturbative manner, using the Schwinger-Dyson (SD) formalism in (scalar) QCD. First, we review dynamical quark-mass generation in QCD in the SD approach as a typical fermion-mass generation via spontaneous chiral-symmetry breaking. Second, using the SD formalism for scalar QCD, we investigate the scalar diquark, a bound-state-like object of two quarks, and its mass generation, which is clearly non-chiral-origin. Here, the scalar diquark is treated as an extended colored scalar field, like a meson in effective hadron models, and its effective size R is introduced as a form factor. As a diagrammatical difference, the SD equation for the scalar diquark has an additional 4-point interaction term, in comparison with the single quark case. The diquark size R is taken to be smaller than a hadron, R ~ 1 fm, and larger than a constituent quark, R ~ 0.3 fm. We find that the compact diquark with R ~ 0.3 fm has a large effective mass of about 900 MeV, and therefore such a compact diquark is not acceptable in effective models for hadrons. We also consider the artificial removal of 3- and 4-point interaction, respectively, to see the role of each term, and find that the 4-point interaction plays the dominant role of the diquark self-energy. From the above two different cases, quarks and diquarks, we guess that the mass generation of colored particles is a general result of non-perturbative gluonic dressing effect.
文摘In view of the properties of mesons in hot strongly interacting matter, the properties of the solutions of the truncated Dyson-Schwinger equation for the quark propagator at finite temperatures within the rainbow-ladder approximation are analysed in some detail. In Euclidean space within the Matsubara imaginary time formalism, the quark propagator is not longer a O(4) symmetric function and possesses a discrete spectrum of the fourth component of the momentum. This makes the treatment of the Dyson-Schwinger and Bethe-Salpeter equations conceptually different from the vacuum and technically much more involved. The question whether the interaction kernel known from vacuum calculations can be applied at finite temperatures remains still open. We find that, at low temperatures, the model interaction with vacuum parameters provides a reasonable description of the quark propagator, while at temperatures higher than a certain critical value T<sub>c </sub>the interaction requires stringent modifications. The general properties of the quark propagator at finite temperatures can be inferred from lattice QCD (LQCD) calculations. We argue that, to achieve a reasonable agreement of the model calculations with that from LQCD, the kernel is to be modified in such a way as to screen the infra-red part of the interaction at temperatures larger than T<sub>c </sub>. For this, we analyse the solutions of the truncated Dyson-Schwinger equation with existing interaction kernels in a large temperature range with particular attention on high temperatures in order to find hints to an adequate temperature dependence of the interaction kernel to be further implemented in the Bethe-Salpeter equation for mesons. This will allow investigating the possible in medium modifications of the meson properties as well as the conditions of quark deconfinement in hot matter.
基金supported by the National Natural Science Foundation of China under Contract Nos.11435001 and 11775041the National Science Foundation of China under Grants No.12175007 and No.12247107。
文摘We solved the Dyson–Schwinger(DS)equations for a two-flavor system with symmetry to study its flavor mixing effects.Initially,we employed the point interaction model and bare vertex approximation to reveal the structure of the solutions.Using the point interaction model,the DS equations can be solved analytically,and we found that these solutions can be classified into three groups,each forming an ellipse.These solutions exhibit SO(2)symmetry,while the original SU(2)symmetry at the Lagrangian level is dynamically broken to SO(2),corresponding to the emergence of flavor mixing effects.However,this flavor mixing effect does not manifest in the final physical state.By utilizing the system's SO(2)symmetry,we can diagonalize the propagators of the DS equations,eliminating the flavor mixing effect but causing the originally degenerate masses at the Lagrangian level to split.These mass eigenstates have identical quantum numbers but different masses.If we can correspond these to quark particles of different generations,we can explain why the three generations of quarks have different masses and obtain the corresponding quark mass spectrum.Finally,we provide the corresponding numerical results using a more realistic interaction model.
基金Supported by the National Natural Science Foundation of China(NSFC)(12375140)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(G1323523064)。
文摘We perform a potential analysis for the holographic Schwinger effect in spinning Myers-Perry black holes.We compute the potential between the produced pair by evaluating the classical action of a string attached on a probe D3-brane at an intermediate position in the AdS bulk.We find that increasing the angular momentum reduces the potential barrier,thus enhancing the Schwinger effect,consistent with previous findings obtained via the local Lorentz transformation.In particular,these effects are more visible for the particle pair lying in the transversal plane compared with that along the longitudinal orientation.In addition,we discuss how the Schwinger effect changes with the shear viscosity to entropy density ratio at strong coupling under the influence of angular momentum.
