CHIRAL ANOMALY AND UNAMBIGUOUS TERMS OF EXACT SCALE BEHAVIOR

We perform new explicit and regularization-independent calculations of < AV > amplitude in QED₁₊₁ and amplitude in QED₁₊₃ respectively to reinvestigate the anomaly problem. A kind of finite and unambiguous terms of exact scale behavior (in momentum space) is found to be responsible for the anomalies both in QED₁₊₁ and QED₁₊₁. They come from logarithmically divergent momentum integrals in contrast with the usual knowledge for triaugle anomaly in QED₁₊₃. In QED₁₊₁, this term is also responsible for photon mass generation. Some implications and possible relations with other aspects of anomaly are discussed.     

Static potential of a point charge in reduced QED<Subscript>3+1</Subscript>

The potential of a point source placed on a flat surface is calculated in the context of reduced QED₃₊₁, and the effective charge behavior is investigated with allowance for the polarization of vacuum. Both approximate analytical and numerical methods are used in calculations. It is established that the behavior of the examined potential at short and long distances from the source does not deviate significantly from the Coulomb behavior of vacuum massless and massive fermions. Other deviations of the results obtained from the well-known standard QED₃₊₁ and QED₂₊₁ data are also discussed.     

Phase transition in three-dimensional quantum electrodynamics at <Emphasis Type="Italic">T</Emphasis> ≠ 0

Dynamic mass generation in 3D quantum electrodynamics (QED₃) is considered at T ≠ 0. To solve the Schwinger–Dyson equation for the Matsubara electron Green’s function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED₃ at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED₃, at T = 0 in QED₄, and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger–Dyson equation are of the same orders of magnitude.     

An alternative approach to dynamical mass generation in QED3

Some quantum properties of QED₃ are studied with the help of an exact evolution equation of the effective action with the bare fermion mass. The resulting effective theory and the occurrence of a dynamical mass are discussed in the framework of the gradient expansion.     

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED₂ with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED₂ with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess-Zumino field replicates the theory, changing neither its algebraic content nor its physical content.     

Admissibility of the axial gauge in QED2

The question recently raised by Tyburski as to whether the axial gauge can be used in two-dimensional quantum electrodynamics is examined. It is shown that even if the arguments leading to A₁≠0 are accepted, the consequences is no more than the existence of an uncoupled massless field in the theory. Thus QED₂ calculations based on the axial gauge do not require reconsideration.     

Quantizing QED2 on the light-cone

The method of discretized light-cone quantization (DLCQ) is applied to quantum electrodynamics in one space and one time dimension (QED₂) with different initial conditions. This leads to different representations of the operators of the constants of motion. Within the fermion-antifermion approximation we perform analytically the transition to the continuum limit and show that the discrete massive and massless representations are equivalent. We compare a semiclassical calculation of the number of bound states with the results obtained in the continuum limit. Furthermore a discrete bosonized version of QED₂ is discussed.     

Analytic study of θ vacua on the lattice

A new definition of the topological charge density for four-dimensional lattice gauge theory is given. Using a systematic expansion we find a cusp in the vacuum energy at θ = π signaling the spontaneous breaking of CP there. Unlike its two-dimensional analogue (QED₂), QCD confines at θ = π. As a by-product an expression for the topological mass term for (2+1)-dimensional lattice gauge theory is obtained.     

Discussing the U(1)-Problem of QED2without Instantons

We construct QED₂with mass and flavor and an extra Thirring term. The vacuum expectation values are carefully decomposed into clustering states using the U(1)-axial symmetry of the considered operators and a limiting procedure. The properties of the emerging expectation functional are compared to the proposedθ-vacuum of QCD. The massive theory is bosonized to a generalized Sine–Gordon model (GSG). The structure of the vacuum of QED₂manifests itself in symmetry properties of the GSG. We study the U(1)-problem and derive a Witten–Veneziano-type formula for the masses of the pseudoscalars determined from a semiclassical approximation.     

Fermionic representation of the Wess-Zumino term and the chiral Schwinger model

The quantum structure of the chiral Schwinger model is studied by fermionization of the Wess-Zumino field. The model contains a hidden parameter a reflecting the ambiguity in the definition of the gauge anomaly. It is shown that, for the special value a = 2, this chiral model is equivalent to massless QED₂ in the sence that they share the same gauge field and the same (left-handed) chiral fermion. The fermionic representation of the Wess-Zumino term provides a natural way to summarize the current algebras and yields a regularization-independent current-algebraic characterization of the model.     

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED3

Elementary-particle Physics and Field Theory

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED₃     

Double hadron lepto-production in the current and target fragmentation regions

We study the inclusive production of two hadrons in deep inelastic processes, ?N→?h₁h₂X, with h₁ in the current fragmentation region (CFR) and h₂ in the target fragmentation region (TFR). Assuming a factorized scheme, the recently introduced polarized and transverse momentum dependent fracture functions couple to the transverse momentum dependent fragmentation functions. This allows the full exploration of the fracture functions for transversely polarized quarks. Some particular cases are considered.     

On the character of chiral symmetry breaking and fermion vacuum structure in QED<Subscript>3</Subscript>

Equation for the Bethe-Salpeter wave function of the Goldstone boson in QED₃ is considered in the ladder approximation with the use of the Landau gauge for the photon propagator. With the help of standard simplifications, the existence of nonzero solutions for this equation is demonstrated, which testifies to the production of the above-described boson in the process of chiral symmetry breaking. At the same time, it is demonstrated that only one of the entire set of solutions describing the Goldstone boson corresponds to the stable ground state; this solution has the greatest fermion mass. In the remaining cases, the compound boson state with zero mass is excited, and all other states having smaller energies appear tachyon states and hence are unstable. The fermion condensate is calculated; it is demonstrated that in the examined case, it is finite. Based on the foregoing, conclusions are drawn about spontaneous rather than dynamic character of chiral symmetry breaking in QED₃, complex structure of fermion vacuum for the examined model, and at the same time, simple structure of the massive phase vacuum.     

The transverse momentum of partons in large pT processes

An approximate method is used to investigate the effects of parton transverse momentum in large p_T particle production within the framework of hard scattering models. We derive an approximate expression for the mean bias towards the trigger of each of the two participating partons and find that event one of the partons is biased more than the other, even with a 90° trigger. We treat the transverse momentum of partons and their closely related off-mass-shell behaviour as a perturbation in the equation for the single-particle inclusive cross section, and then expand in a Taylor series. We calculate the first non-zero correction term and find that to this order, the cross section is increased by parton transverse momentum effects by typically a factor of 1.7 for p_T = 3 GeV/c with 〈k_T〉 = 500 MeV/c, or 1.25 for p_T = 3 GeV/c with 〈k_T〉 = 300 MeV/c, and that the correction decreases rapidly with increasing p_T.     

12C(e,e′ p) missing momentum distributions in HF-Sk3 and RPA-Sk3 continuum theories

We study the momentum distribution or reduced cross-section for electron induced 1p _3/2 proton knockout from¹²C in parallel kinematics. We refer to continuum self-consistent HF-Sk 3 and RPA-Sk 3 theories with a full treatment of the one-nucleon energy continuum. The PWIA limit is also shown. The¹²C(e, e′p ₀) missing momentum distribution is analyzed in connection with the energy dependence at fixed momentum transfer of the¹²C(e, e′) longitudinal and transverse responses. We compare our theoretical results with the available experimental data.     

Asymmetric modulation of the transverse current effect of charge-density wave in the blue bronze K0.3MoO3

The effect of a transverse single-particle current (I_x) on the charge-density wave (CDW) dynamics in the blue bronze K_0.3MoO₃ was reported. We found that the modulation of I–V characteristics are asymmetric to the polarity of the transverse current, possibly due to an additional longitudinal electric field (E_add) caused by the slight unbalance of the two transverse current probes. Our result seems inconsistent in some ways with the recent study by Artemenko et al.     

Calculation of Particle-Number Susceptibility of QED3 at Finite Temperature

Based on the external field approach and the differential form of Ward identity, we derive a more compact formula for the particle-number susceptibility in QED3 at finite temperature. Using the zero frequency approximation the numerical value of the particle-number susceptibility is calculated in the Dyson-Schwinger approach for the case that the number of fermion flavours equals one and two, respectively. An enhanced fluctuation of the particlenumber density is observed across the transition temperature, which should be an essential characteristic of chiral phase transition in QED3.     

Quark confinement and instanton-like Euclidean field configurations

We introduce the concept of “c instanton” configuration and show that the QED₂ confinement may be understood as a saturation of the functional integrals in terms of such new configuration.