Effect of Fermion Velocity on Phase Structure of QED3

Dynamical chiral symmetry breaking (DCSB) in thermal QED₃ with fermion velocity is studied in the framework of Dyson-Schwinger equations. By adopting instantaneous approximation and neglecting the transverse component of gauge boson propagator at finite temperature, we numerically solve the fermion self-energy equation in the rainbow approximation. It is found that both DCSB and fermion chiral condensate are suppressed by fermion velocity. Moreover, the critical temperature decreases as fermion velocity increases.     

Influence of Finite Chemical Potential on Critical Boson Mass in QED3

Using the coupled Dyson-Schwinger equation for the fermion propagator at finite chemical potential μ, we investigate the fermion chiral condensate when the gauge boson mass is nonzero in QED3. We show that the chiral symmetry restores when the boson mass is large enough, and the critical boson mass depends little on μ.     

A New Approach for Calculating Spin Susceptibility in QED3

Based on the study of the linear response of the fermion propagator to the presence of an external scalar field, a new method for calculating the staggered spin susceptibility in QED3 is presented, in which the influence of the full vertex function is included. The numerical values of the staggered spin susceptibility are calculated within the framework of the rainbow-ladder approximation of the Dyson-Schwinger approach. A comparison between the result calculated using the full vertex and that using the bare vertex is given.     

有限温下三维QED中费米速度对费米子手征凝聚的影响（英文）

三维QED 具有两个和QCD类似的性质:动力学手征对称破缺和禁闭。为了研究动力学手征对称破缺,基于彩虹近似,在Dyson-Schwinger 方程框架下,通过迭代求解有限温下的费米子自能方程,讨论了不同的费米速度下费米子手征凝聚与费米子味数之间的关系。发现在有限温下,对于固定的费米子味数,费米手征凝聚随费米速度的变大而单调减小。Analogous to Quantum QCD, QED₃ has two interesting features: dynamical chiral symmetry breaking (DCSB) and confinement. By adopting the rainbow approximation, we numerically solve the fermion self-energy equation at finite temperature in the framework of Dyson-Schwinger equations and discuss the relation between chiral condensate and fermion flavor for several fermion velocities in the finite temperature QED₃. It is found that the fermion chiral condensate decreases monotonically with the fermion velocity increasing for a fixed N at finite temperature.     

Running flavor number and asymptotic freedom in the normal phase of QED

In the normal phase (where no dynamical fermion mass generation occurs) of the D-dimensional quantum electrodynamics with N_f flavors of fermions, we derive an integral equation which should be satisfied by (the inverse of) the wave function renormalization of the fermion in the Landau gauge. For this we use the inverse Landau-Khalatnikov transformation connecting the nonlocal gauge with the Landau gauge. This leads to a similar equation for the running flavor number in the framework of the 1/N_f resumed Schwinger-Dyson equation. Solving the equation analytically and numerically, we study the infrared behavior and the critical exponent of the 3-dimensional QED (QED₃). This confirms that the flavor number in QED₃ runs according to the β function which is consistent with the asymptotic freedom as that in 4-dimensional QCD.     

Algebraic renormalization of parity-preserving QED3 coupled to scalar matter I: unbroken case

In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED₃ coupled to scalar matter in the symmetric regime, where the scalar assumes vanishing vacuum expectation value, = 0. The model shows to be stable under radiative corrections and anomaly free.     

Critical Number of Fermion Flavors at Finite Chemical Potential in QED3

We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S（p） = iγ.p^-A（p^-2） ＋ B（ p^-2） with p^-μ= （p^-1p3 ＋ iμ）. Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.     

三维QED中的几个重要问题（英文）

三维量子电动力学是一种看上去比较简单的Abel 类型的非微扰系统,其本身却有很多需要澄清的基本问题。从该系统是否具有密度依赖性,有限温下是否具有动力学自发对称破却以及规范玻色子可否具有质量这三方面出发,阐述了对三维量子电动力学一些基本问题的看法。Quantum electrodynamics in (2+1) dimensions (QED₃) is an important nonperturbative system. This seems relatively simple Abel system, there are several issues that need to be clarified: whether or not the partition function of the system depends on chemical potential; whether or not there exists dynamical chiral symmetric breaking; whether or not the boson can acquires nonzero mass. In this paper, we give an in sight of the traits of QED₃ from the dependence of density, temperature and massive boson to discuss those problems.     

Propagators and Masses of Light Quarks

Based on Dyson-Schwinger equations in “rainbow” approximation, fully dressed confining quark propagator is obtained, and then the masses of light quarks (mu, md, and ms) are derived from the fully dressed confining quark propagator. At the same time, the local and non-local quark vacuum condensates as well as the quark-gluon mixed condensate are also predicted. Furthermore, the quark masses are also deduced from the Gell-Mann-Oakes-Renner relation and chiral perturbative theory. The results from different methods are consistent with each other.     

About the chiral symmetry breaking in QED<Subscript>3</Subscript>

The problem of the chiral symmetry breaking in QED₃ is considered by solving the Schwinger–Dyson equation for the fermion propagator in the ladder approximation using the Landau gauge for the photon propagator. Within the framework of the indicated approximation, different simplifications that allow expressions for the fermion mass function to be retrieved in an explicit form are analyzed. The results obtained are compared with the data of numerical analysis. It appears that the neglect of higher Gegenbauer harmonics in the kernel of the initial integral equation for the fermion mass function influences the dynamic mass value and the asymptotics of the mass function only weakly. On the other hand, it is established that the conclusion about a complicated structure of the fermion vacuum of the massive phase is an artifact of linearization of the Schwinger–Dyson equation kernel: consideration of the kernel nonlinearity yields a simple massive phase structure of the fermion vacuum.     

Critical Mass of Gauge Boson in Rainbow QED3

In three-dimensional quantum electrodynamics (QED₃) with a massive gauge boson, we investigate the coupled Dyson-Schwinger equations for the fermion and photon propagators in the rainbow approximation, and obtain the critical gauge boson mass for various numbers of the fermion flavors. A comparison with the previous results is presented.     

The quark propagator from the Dyson-Schwinger equations: (I). The chiral solution

Within the framework of the Dyson-Schwinger equations in the axial gauge, and using a truncation procedure which respects the Ward-Takahashi identities, we study the effect that nonperturbative glue has on the quark propagator. We show that within this truncation scheme, the requirement of matching perturbative QCD at high momentum transfer leads to a multiplicatively renormalisable equation. Technically, the matching with perturbation theory is accomplished by the introduction of a transverse part to the quark-gluon vertex. In the case of an analytic gluon propagator, this truncation scheme can lead to chiral symmetry breaking only after the introduction of such a transverse vertex: massless solutions do not exist beyond a critical value of as. Using the gluon propagator that we previously obtained, we obtain small corrections to the quark propagator, which keeps a pole at the origin in the chiral phase.     

Gauge Invariance of a Critical Number of Flavours in QED3

The fermion propagator in an arbitrary covariant gauge can be obtained from the Landau gauge result via a Landau–Khalatnikov–Fradkin transformation. This transformation can be written in a practically useful form in both configuration and momentum space. It is therefore possible to anticipate effects of a gauge transformation on the propagator’s analytic properties. These facts enable one to establish that if a critical number of flavours for chiral symmetry restoration and deconfinement exists in noncompact QED3, then its value is independent of the gauge parameter. This is explicated using simple forms for the fermion–photon vertex and the photon vacuum polarisation. The illustration highlights pitfalls that must be avoided in order to arrive at valid conclusions. Landau gauge is seen to be the covariant gauge in which the propagator avoids modification by a non-dynamical gauge-dependent exponential factor, whose presence can obscure truly observable features of the theory.     

Instability at the origin in (2+1)-dimensional QED

Stability at the origin in (2+1)-dimensional QED withN four-component Dirac fermions is studied by keeping the leading order terms in 1/N in the effective potential. It is shown that the effective potential in the direction of fermion wave-function renormalization is always unstable for any flavor numberN, which reconfirms that chiral symmetry is broken for anyN.     

Long-distance behaviour of fermion propagators in the chiral Schwinger model

The chiral Schwinger model's fermionic sector is studied by comparing the fermion propagator of the original Jackiw-Rajaraman formulation with a propagator in the gauge invariant formulation. The main difference consists in the existence of fermionic single particle states in the original formulation, while there are no such states in the gauge invariant formulation. It is suggested that this difference is caused by renormalization, which changes the Hilbert space.     

Infrared behaviour of propagators and vertices

We elucidate constraints imposed by confinement and dynamical chiral symmetry breaking on the infrared behaviour of the dressed-quark and -gluon propagators, and dressed-quark-gluon vertex. In covariant gauges the dressing of the gluon propagator is completely specified by , where Π(k²) is the vacuum polarisation. In the absence of particle-like singularities in the dressed-quark-gluon vertex, extant proposals for the dressed-gluon propagator that manifest and neither confine quarks nor break chiral symmetry dynamically. This class includes all existing estimates of via numerical simulations.     

Instantons and the chiral phase transition

We examine the role of instantons in the zero-temperature chiral phase transition in an SU(N) gauge theory. For a range of N_f (the number of fermion flavors) depending on N, the theory exhibits an infrared fixed point at coupling _*. As N_f decreases, _* increases, and it eventually exceeds a critical value sufficient to trigger chiral symmetry breaking. For the case N = 2, we estimate the critical values of N_f and _* due to instantons by numerically solving a gap equation with an instanton-generated kernel. We find instanton effects of strength comparable to that of gluon exchange.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Perturbative chiral nucleon-nucleon potential for the 3P0 partial wave

We study perturbativeness of chiral nuclear forces in the ³P₀ channel. In previous works, the focus has been on the one-pion exchange, and the applicable window of perturbative pion exchanges has been shown to span from the threshold to center-of-mass momentum k≃180 MeV. We will examine, instead, whether the cancellation of short- and long-range parts can sufficiently soften the ³P₀ chiral force to make it more amenable to perturbation theory. The result is encouraging, as the combined ³P₀ force is shown to be perturbative up to k≃280 MeV, covering many nuclear-structure calculations.     

Radiative Corrections in the Boulatov-Ooguri Tensor Model: The 2-Point Function

The Boulatov-Ooguri tensor model generates a sum over spacetime topologies for the D-dimensional BF theory. We study here the quantum corrections to the propagator of the theory. In particular, we find that the radiative corrections at the second order in the coupling constant yield a mass renormalization. They also exhibit a divergence which cannot be balanced with a counter-term in the initial action, and which usually corresponds to the wave-function renormalization.