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
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 study the Schwinger mechanism in the presence of an additional uniformly oriented,weak super Gaussian of integer order 4 N+2.Using the worldline approach,we determine the relevant critical points to compute the lea...We study the Schwinger mechanism in the presence of an additional uniformly oriented,weak super Gaussian of integer order 4 N+2.Using the worldline approach,we determine the relevant critical points to compute the leading order exponential factor analytically.We show that increasing the parameter N gives rise to a strong dynamical enhancement.For N=2,this effect turns out to be larger compared to a weak contribution of the Sauter type.For higher orders,specifically,for the rectangular barrier limit,i.e.N→∞,we approach the Lorentzian case as an upper bound.Although the mentioned backgrounds significantly differ in Minkowski spacetime,we show that the found coincidence applies due to identical reflection points in the Euclidean instanton plane.In addition,we also treat the background in perturbation theory following recent ideas.By doing so,we show that the parameter N determines whether the weak contribution behaves perturbatively or nonperturbatively with respect to the field strength ratio,and,hence,reveals an interesting dependence on the background shape.In particular,we show that for backgrounds,for which higher orders in the field strength ratio turn out to be relevant,a proposed integral condition is not fulfilled.In view of these findings,the latter may serve as an indicator for the necessity for higher-order contributions.展开更多
In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory （QFT） incorporating the minimal length. We first study the Schwinger mechanism for scalar fields ...In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory （QFT） incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the deformed QFT. The same calculations are then performed in the case of Dirac particles. Finally, we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length.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
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 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the support of the Collaborative Research Center SFB 676 of the DFG.
文摘We study the Schwinger mechanism in the presence of an additional uniformly oriented,weak super Gaussian of integer order 4 N+2.Using the worldline approach,we determine the relevant critical points to compute the leading order exponential factor analytically.We show that increasing the parameter N gives rise to a strong dynamical enhancement.For N=2,this effect turns out to be larger compared to a weak contribution of the Sauter type.For higher orders,specifically,for the rectangular barrier limit,i.e.N→∞,we approach the Lorentzian case as an upper bound.Although the mentioned backgrounds significantly differ in Minkowski spacetime,we show that the found coincidence applies due to identical reflection points in the Euclidean instanton plane.In addition,we also treat the background in perturbation theory following recent ideas.By doing so,we show that the parameter N determines whether the weak contribution behaves perturbatively or nonperturbatively with respect to the field strength ratio,and,hence,reveals an interesting dependence on the background shape.In particular,we show that for backgrounds,for which higher orders in the field strength ratio turn out to be relevant,a proposed integral condition is not fulfilled.In view of these findings,the latter may serve as an indicator for the necessity for higher-order contributions.
基金Supported by National Natural Science Foundation of China under Grant Nos.11005016,11175039,and 11375121the Fundamental Research Funds for the Central Universities
文摘In this paper, we investigate effects of the minimal length on the Schwinger mechanism using the quantum field theory （QFT） incorporating the minimal length. We first study the Schwinger mechanism for scalar fields in both usual QFT and the deformed QFT. The same calculations are then performed in the case of Dirac particles. Finally, we discuss how our results imply for the corrections to the Unruh temperature and the Hawking temperature due to the minimal length.
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.
