Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potentiM for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A（p^2） in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics （QCD）, we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Cornwall-Jackiw-Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function A(p2) in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential, which will be a useful means to research chiral phase transition in QCD in the real-time formalism.     

Real-Time Thermal Schwinger-Dyson Equation for Quark Self-energy in Landau Gauge

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(p2)p - B(p2), we argue that, when temperature T is lower than the given infrared momentum cutoff pc, A(p2) = 1 is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.     

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.     

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.     

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model

The discrete symmetry breaking and possible restoration at finite temperature T are analyzed in 20 Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature T_c = 0.567m(O), m(0) is the dynamical fermion mass at T = 0, shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the ln(T_c/T) behavior of m² at T ≤ T_c can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.     

The fermion propagator matrix in lattice QCD

The fermion propagator matrix is introduced and analyzed in lattice QCD. It can be related directly to the inverse of the fermion matrix and is similar in some ways to the transfer matrix. It is shown how the Lanczos algorithm can be used to diagonalise it and this is illustrated by calculating the eigenvalues on 4⁴ QCD configurations and relating the results to finite-density calculations of the chiral condensate and quark currents. This sets the groundwork for calculations on larger lattices which should, in principle, give the hadron spectrum in a way which has some advantages over usual methods.     

Nontopological finite temperature induced fermion number

We show that while the zero temperature induced fermion number in a chiral sigma model background depends only on the asymptotic values of the chiral field, at finite temperature the induced fermion number depends also on the detailed shape of the chiral background. We resum the leading low temperature terms to all orders in the derivative expansion, producing a simple result that can be interpreted physically as the different effect of the chiral background on virtual pairs of the Dirac sea and on the real particles of the thermal plasma. By contrast, for a kink background, not of sigma model form, the finite T induced fermion number is temperature dependent but topological.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

Study of the gluon propagator in the large-Nf limit at finite temperature and chemical potential for weak and strong couplings

At finite temperature and chemical potential, the leading-order (hard-thermal-loop) contributions to the gauge-boson propagator lead to momentum-dependent thermal masses for propagating quasiparticles as well as dynamical screening and Landau damping effects. We compare the hard-thermal-loop propagator with the complete large-N_f gluon propagator, for which the usually subleading contributions, such as a finite width of quasiparticles, can be studied at nonperturbatively large effective coupling. We also study quantitatively the effect of Friedel oscillations in low-temperature electrostatic screening.     

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.     

A Modified Approach for Calculating Dressed Quark Propagator at Finite Chemical Potential

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the full inverse quark propagator at finite chemical potential is analytic in the neighborhood of μ = 1, it is proved that the dressed quark propagator at finite chemical potential μ can be written as G0^-1 [μ] =iγ·p↑-A（p↑-^2） ＋B（p↑-^2） with p↑-μ= （p↑-p4 ＋iμ）. From the dressed quark propagator at finite chemical potential in Munczek model the bag constant of a baryon and the scalar quark condensate are evaluated. A comparison with previous results is given.     

Quantum Electrodynamics at High Temperature: (I). One Spatial Dimension

The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed at high temperature to all orders of perturbation theory. The imaginary-time formalism is used. The photon self-energy and propagator at finite temperature with vanishing frequency are given to second order of perturbation theory. Based upon them, an improved perturbation theory which incorporates Debye screening if formulated. In the infinite-temperature limit, the photon sector becomes equivalent to a massive scalar boson field plus a masslees pure gauge field and both are decoupled: all connected Green's functions with given external momenta much smaller than the temperature and containing, at least, one closed fermion loop with four or more vertices vanish. An approximate generating functional yielding all leading high-temperature corrections to all connected Green's functions is preaented. The Iast result leads to establish for one spatial dimension a conjecture of Gross, Pisarski and Yaffe regarding the reduction of QED to a sort of ϕ⁴ theory at high temperature. The leading high temperature contribution to the thermodynamic potential to all perturbativc orders: i) is given in terms of the dominant high temperature contribution to the two-point photon Green's function for zero frequency, ii) is shown to be both ultraviolet and infrared finite.     

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.     

Absence of species doubling in finite-element quantum electrodynamics

In this Letter, it will be demonstrated explicitly that the finite-element formulation of quantum electrodynamics is free from fermion doubling. We do this by (1) examining the lattice fermion propagator and using it to compute the one-loop vacuum polarization on the lattice, and (2) by an explict computation of vector and axial-vector current anomalies for an arbitrary rectangular lattice in the Schwinger model. There it is shown that requiring that the vector current be conserved necessitates the use of a square lattice, in which case the axial-vector current is anomalous.     

Comment on “Causal structure of the thermal propagator in real time formalisms”

Some comments are made on a recent work by Lutz and Kunihiro on the time-ordered fermion propagator at finite temperature.     

Electron and quasiparticle exponents of Haldane-Rezayi state in non-abelian fractional quantum Hall theory

The quasiparticle propagator of the Haldane-Rezayi (HR) fractional quantum Hall (FQH) state is calculated, based on a chiral fermion model (or a Weyl fermion model) equipped with a hidden spin SU(2) symmetry. The spectrum of the chiral fermion model for each total spin and total momentum is shown to be identical to that of the SU(2) c = −2 model introduced to describe the edge spectrum of the HR state.     

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.     

Improved Monte Carlo methods for fermions

We describe an improved version of the Kuti-Von Neumann-Ulam algorithm useful for fermion contributions in lattice field theories. This is done by sampling the Neumann series for the propagator, which may be thought of as a sum over a set of weighted paths between two points on the lattice. Rather than selecting paths by a locally determined random walk, we average over sets of paths globally preselected for their importance in evaluating the few needed elements of the inverse. We also describe a method for the calculation of ratios of fermion determinants which is considerably less time consuming than the conventional one.